]>
2019
12
7
ISSN 2008-1898
90
Comparison of the best approximation of holomorphic functions from Hardy space
Comparison of the best approximation of holomorphic functions from Hardy space
en
en
We compare the best approximations of holomorphic functions in the Hardy space \(H^1\) by algebraic polynomials and trigonometric
polynomials. Particulary, we establish a class of functions \(f\in H^1\) for which the best trigonometric approximation do not coincide with the best algebraic approximation.
412
419
F. G.
Abdullayev
Mersin University
Kyrgyz--Turkish Manas University
Turkey
Kyrgyzstan
fabdul@mersin.edu.tr
V. V.
Savchuk
Institute of Mathematics of NAS of Ukraine
Ukraine
savchuk@imath.kiev.ua
D.
Simsek
Kyrgyz--Turkish Manas University
Kyrgyzstan
dagistan.simsek@manas.edu.kg
Best approximation
Hardy space
non-negative trigonometric polynomials
Article.1.pdf
[
[1]
F. G. Abdullayev, G. A. Abdullayev, V. V. Savchuk, Best approximation of holomorphic functions from Hardy space in terms of Taylor coefficient, , (to appear in Filomat.), -
##[2]
S. Y. Al’per , On the Best Mean First-degree Approximation of Analytic Functions on Circle (Russian), Dokl. Akad. Nauk S.S.S.R., 153 (1963), 503-506
##[3]
A. A. Pekarskii, Comparison of the Best Uniform Approximations of Analytic Functions in the Disk and on Its Boundary (Russian), translated from Tr. Mat. Inst. Steklova, 255 (2006), 227-232
##[4]
V. V. Savchuk, Best Approximation of Cauchy–Szegö Kernel in the Mean on Circle (Ukrainian), Ukr. Mat. Zh., 70 (2018), 708-714
##[5]
V. V. Savchuk, S. O. Chaichenko, Addendum to a theorem of F. Wiener about sieve (Ukrainian), Praci Instytutu Matematyky NAN Ukrainy, 12 (2015), 262-272
##[6]
V. V. Savchuk, M. V. Savchuk, S. O. Chaichenko, Approximation of Analytic Functions byde Valle Poussin sums (Ukrainian), Matematychni Studii, 34 (2010), 207-219
]
Stability of discrete-time HIV dynamics models with long-lived chronically infected cells
Stability of discrete-time HIV dynamics models with long-lived chronically infected cells
en
en
This paper studies the global dynamics for discrete-time HIV infection models.
The models integrate both long-lived chronically infected and short-lived
infected cells. The HIV-susceptible incidence rate is taken as bilinear,
saturation and general function. We discretize the continuous-time models by
using nonstandard finite difference scheme. The positivity and boundedness of
solutions are established. The basic reproduction number is derived. By using
Lyapunov method, we prove the global stability of the models. Numerical
simulations are presented to illustrate our theoretical results.
420
439
A. M.
Elaiw
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
a_m_elaiw@yahoo.com
M. A.
Alshaikh
Department of Mathematics, Faculty of Science
Department of Mathematics, Faculty of Science
King Abdulaziz University
Taif University
Saudi Arabia
Saudi Arabia
matukaalshaikh@gmail.com
HIV infection
short-lived infected cells
long-lived infected cells
global stability
Lyapunov function
Article.2.pdf
[
[1]
D. S. Callaway, A. S. Perelson, HIV-1 infection and low steady state viral loads, Bull. Math. Biol., 64 (2002), 29-64
##[2]
R. V. Culshaw, S. G. Ruan, A delay-differential equation model of HIV infection of CD4+ T-cells, Math. Biosci., 165 (2000), 27-39
##[3]
R. V. Culshaw, S. G. Ruan, G. Webb, A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay, J. Math. Biol., 46 (2003), 425-444
##[4]
D. Q. Ding, X. H. Ding, Dynamic consistent non-standard numerical scheme for a dengue disease transmission model , J. Difference Equ. Appl., 20 (2014), 492-505
##[5]
D. Ding, W. Qin, X. Ding, Lyapunov functions and global stability for a discretized multigroup SIR epidemic model, Discrete Contin. Dyn. Syst. Ser. B, 20 (2015), 1971-1981
##[6]
A. Dutta , P. K. Gupta, A mathematical model for transmission dynamics of HIV/AIDS with effect of weak CD4+ T cells, Chinese J. Phys., 56 (2018), 1045-1056
##[7]
A. M. Elaiw, Global properties of a class of HIV models, Nonlinear Anal. Real World Appl., 11 (2010), 2253-2263
##[8]
A. M. Elaiw , Global properties of a class of virus infection models with multitarget cells, Nonlinear Dynam., 69 (2012), 423-435
##[9]
A. M. Elaiw, N. A. Almuallem, Global properties of delayed-HIV dynamics models with differential drug efficacy in cocirculating target cells, Appl. Math. Comput., 265 (2015), 1067-1089
##[10]
A. M. Elaiw, N. A. Almuallem, Global dynamics of delay-distributed HIV infection models with differential drug efficacy in cocirculating target cells, Math. Methods Appl. Sci., 39 (2016), 4-31
##[11]
A. M. Elaiw, N. H. AlShamrani, Stability of a general delay-distributed virus dynamics model with multi-staged infected progression and immune response, Math. Methods Appl. Sci., 40 (2017), 699-719
##[12]
A. M. Elaiw, I. A. Hassanien, S. A. Azoz, Global stability of HIV infection models with intracellular delays, J. Korean Math. Soc., 49 (2012), 779-794
##[13]
A. M. Elaiw, A. A. Raezah, Stability of general virus dynamics models with both cellular and viral infections and delays, Math. Methods Appl. Sci., 40 (2017), 5863-5880
##[14]
A. M. Elaiw, S. A. Azoz, Global properties of a class of HIV infection models with Beddington-DeAngelis functional response, Math. Methods Appl. Sci., 36 (2013), 383-394
##[15]
S. Elaydi, An introduction to Difference Equations, Third ed., Springer, New York (2005)
##[16]
Y. Enatsu, Y. Nakata, Y. Muroya, G. Izzo, A. Vecchio , Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates, J. Difference Equ. Appl., 18 (2012), 1163-1181
##[17]
Y. Geng, J. H. Xu, J. Y. Hou, Discretization and dynamic consistency of a delayed and diffusive viral infection model, Appl. Math. Comput., 316 (2018), 282-295
##[18]
K. Hattaf, A. A. Lashari, B. El Boukari, N. Yousfi, Effect of discretization on dynamical behavior in an epidemiological model, Differ. Equ. Dyn. Syst., 23 (2015), 403-413
##[19]
K. Hattaf, N. Yousfi, A generalized virus dynamics model with cell-to-cell transmission and cure rate, Adv. Difference Equ., 2016 (2016), 1-11
##[20]
K. Hattaf, N. Yousfi, A numerical method for delayed partial differential equations describing infectious diseases, Comput. Math. Appl., 72 (2016), 2741-2750
##[21]
K. Hattaf, N. Yousfi, A numerical method for a delayed viral infection model with general incidence rate, J. King Saud Uni.-Sci., 28 (2016), 368-374
##[22]
K. Hattaf, N. Yousfi , Global properties of a discrete viral infection model with general incidence rate, Math. Methods Appl. Sci., 39 (2016), 998-1004
##[23]
G. Huang, Y. Takeuchi, W. Ma, Lyapunov functionals for delay differential equations model of viral infections, SIAM J. Appl. Math., 70 (2010), 2693-2708
##[24]
A. Korpusik, A nonstandard finite difference scheme for a basic model of cellular immune response to viral infection, Commun. Nonlinear Sci. Numer. Simul., 43 (2017), 369-384
##[25]
J. P. Lasalle, The stability and control of discrete processes, Springer-Verlag, New York (1986)
##[26]
B. Li, Y. M. Chen, X. J. Lu, S. Q. Liu, A delayed HIV-1 model with virus waning term, Math. Biosci. Eng., 13 (2016), 135-157
##[27]
M. Y. Li, L. C.Wang, Backward bifurcation in a mathematical model for HIV infection in vivo with anti-retroviral treatment, Nonlinear Anal. Real World Appl., 17 (2014), 147-160
##[28]
J. L. Liu, B. Y. Peng, T. L. Zhang, Effect of discretization on dynamical behavior of SEIR and SIR models with nonlinear incidence, Appl. Math. Lett., 39 (2015), 60-66
##[29]
K. Manna, S. P. Chakrabarty, Global stability and a non-standard finite difference scheme for a diffusion driven HBV model with capsids, J. Difference Equ. Appl., 21 (2015), 918-933
##[30]
R. E. Mickens, Nonstandard Finite Difference Models of Differential equations, World Scientific Publishing Co., River Edge (1994)
##[31]
R. E. Mickens, Dynamics consistency: a fundamental principle for constructing nonstandard finite difference scheme for differential equation, J. Difference Equ. Appl., 11 (2005), 645-653
##[32]
P. W. Nelson, J. D. Murray, A. S. Perelson, A model of HIV-1 pathogenesis that includes an intracellular delay, Math. Biosci., 163 (2000), 201-215
##[33]
M. A. Nowak, C. R. M. Bangham , Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74-79
##[34]
C. M. A. Pinto, A. R. M. Carvalho, A latency fractional order model for HIV dynamics, J. Comput. Appl. Math., 312 (2017), 240-256
##[35]
W. D. Qin, L. S. Wang, X. H. Ding, A non-standard finite difference method for a hepatitis b virus infection model with spatial diffusion , J. Difference Equ. Appl., 20 (2014), 1641-1651
##[36]
P. L. Shi, L. Z. Dong, Dynamical behaviors of a discrete HIV-1 virus model with bilinear infective rate, Math. Methods Appl. Sci., 37 (2014), 2271-2280
##[37]
X. Y. Shi, X. Y. Zhou, X. Y. Song , Dynamical behavior of a delay virus dynamics model with CTL immune response, Nonlinear Anal. Real World Appl., 11 (2010), 1795-1809
##[38]
X. Y. Song, A. U. Neumann, Global stability and periodic solution of the viral dynamics, J. Math. Anal. Appl., 329 (2007), 281-297
##[39]
Z. D. Teng, L. Wang, L. F. Nie, Global attractivity for a class of delayed discrete SIRS epidemic models with general nonlinear incidence, Math. Methods Appl. Sci., 38 (2015), 4741-4759
##[40]
L. C. Wang, M. Y. Li , Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells, Math. Biosci., 200 (2006), 44-57
##[41]
J. P. Wang, Z. D. Teng, H. Miao, Global dynamics for discrete-time analog of viral infection model with nonlinear incidence and CTL immune response, Adv. Difference Equ., 2016 (2016), 1-19
##[42]
J. Xu, Y. Geng, J. Hou, A non-standard finite difference scheme for a delayed and diffusive viral infection model with general nonlinear incidence rate, Comput. Math. Appl., 74 (2017), 1782-1798
##[43]
J. H. Xu, J. Y. Hou, Y. Geng, S. X. Zhang, Dynamic consistent NSFD scheme for a viral infection model with cellular infection and general nonlinear incidence, Adv. Difference Equ., 2018 (2018), 1-17
##[44]
Y. Yang, X. S. Ma, Y. H. Li , Global stability of a discrete virus dynamics model with Holling type-II infection function, Math. Methods Appl. Sci., 39 (2016), 2078-2082
##[45]
Y. Yang, J. L. Zhou, Global stability of a discrete virus dynamics model with diffusion and general infection function, Int. J. Comput. Math., 2018 (2018), 1-11
##[46]
Y. Yang, J. L. Zhou, X. S. Ma, T. H. Zhang, Nonstandard finite difference scheme for a diffusive within-host virus dynamics model both virus-to-cell and cell-to-cell transmissions, Comput. Math. Appl., 72 (2016), 1013-1020
##[47]
Y. Zhao, D. T. Dimitrov, H. Liu, Y. Kuang, Mathematical insights in evaluating state dependent effectiveness of HIV prevention interventions, Bull. Math. Biol., 75 (2013), 649-675
##[48]
J. L. Zhou, Y. Yang, Global dynamics of a discrete viral infection model with time delay, virus-to-cell and cell-to-cell transmissions, J. Difference Equ. Appl., 23 (2017), 1853-1868
]
Contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly Sasakian structure
Contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly Sasakian structure
en
en
This paper studies the contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly Sasakian structure. Some Characterization of the existence of these warped product submanifolds are also obtained. We illustrate that the warping function is a harmonic function under certain conditions. Moreover, a sharp estimate for the squared norm of the second fundamental form is investigated, and the equality case is also discussed. The results obtained in this paper generalize the results that have appeared in [I. Hasegawa, I. Mihai, Geom. Dedicata, \({\bf 102}\) (2003), 143--150], [I. Mihai, Geom. Dedicata, \({\bf 109}\) (2004), 165--173}], and [M. Atceken, Hacet. J. Math. Stat., \({\bf 44}\) (2015), 23--32].
440
449
Amira A.
Ishan
Department of Mathematics
Taif University
Kingdom of Saudi Arabia
amiraishan@hotmail.com
Meraj Ali
Khan
Department of Mathematics
University of Tabuk
Kingdom of Saudi Arabia
meraj79@gmail.com
Warped products
CR-submanifolds
nearly Sasakian manifolds
Article.3.pdf
[
[1]
P. Alegre, D. E. Blair, A. Carriazo , Generalized Sasakian space forms, Israel J. Math., 141 (2004), 157-183
##[2]
F. R. Al-Solamy, M. A. Khan, Semi-invariant warped product submanifolds of almost contact manifolds, J. Inequal. Appl., 2012 (2012), 1-12
##[3]
K. Arslan, R. Ezentas, I. Mihai, C. Murathan, Contact CR-warped product submanifolds in Kenmotsu space forms, J. Korean Math. Soc., 42 (2005), 1101-1110
##[4]
M. Atceken, Contact CR-warped product submanifolds in cosymplectic space forms, Collect. Math., 62 (2011), 17-26
##[5]
M. Atceken, Contact CR-warped product submanifolds in Kenmotsu space forms, Bull. Iranian Math. Soc., 39 (2013), 415-429
##[6]
M. Atceken, Contact CR-warped product submanifolds in Sasakian space form, Hacet. J. Math. Stat., 44 (2015), 23-32
##[7]
R. L. Bishop, B. O’Neill, Manifolds of Negative curvature, Trans. Amer. Math. Soc., 145 (1965), 1-49
##[8]
D. E. Blair, Contact manifolds in Riemannian Geometry, Springer-Verlag, Berlin-New York (1976)
##[9]
D. E. Blair, D. K. Showers , Almost contact manifolds with Killing structure tensors II, J. Differential Geometry, 9 (1974), 577-582
##[10]
D. E. Blair, D. K. Showers, K. Yano, Nearly Sasakian structure , Kodai Math. Sem. Rep., 27 (1976), 175-180
##[11]
B.-Y. Chen, CR-submanifolds of a Kaehler manifold I , J. Differential Geom., 16 (1981), 305-323
##[12]
B.-Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds I , Monatsh Math., 133 (2001), 177-195
##[13]
B.-Y. Chen, Pseudo-Riemannian Geometry, \(\delta\)-invariants and Applications, World Scientific Publishing Co. Pte. Ltd., Hackensack (2011)
##[14]
B.-Y. Chen, A survey on geometry of warped product submanifolds, arXiv, 2013 (2013), 1-44
##[15]
I. Hasegawa, I. Mihai, Contact CR-warped product submanifolds in Sasakian manifolds , Geom. Dedicata, 102 (2003), 143-150
##[16]
S.-T. Hong, Warped products and black holes, Nuovo Cimento Soc. Ital. Fis. B, 120 (2005), 1227-1234
##[17]
K. Kenmotsu, Class of almost contact Riemannian manifolds, Tohoku Math. J. , (2), 24 (1972), 93-103
##[18]
M. A. Khan, A. A. Ishan, CR-warped product submanifolds of a generalized complex space form, Cogent Math., 4 (2017), 1-13
##[19]
M. A. Khan, S. Uddin, R. Sachdeva, Semi-invariant warped product submanifolds of cosymplectic manifolds, J. Inequal. Appl., 2012 (2012), 1-13
##[20]
G. D. Ludden, Submanifolds of cosymplectic manifolds, J. Differential Geometry, 4 (1970), 237-244
##[21]
I. Mihai , Contact CR-warped product submanifolds in Sasakain space forms, Geom. Dedicata, 109 (2004), 165-173
##[22]
M.-I. Munteanu, Warped product contact CR-submanifolds of Sasakian space forms, Pubi. Math. Debrecen, 66 (2005), 75-120
]
Optimization of two-step block method with three hybrid points for solving third order initial value problems
Optimization of two-step block method with three hybrid points for solving third order initial value problems
en
en
An optimized two-step hybrid block method for the numerical solution of third-order initial value problems is presented. The method
takes into regard three hybrid points which are selected suitably to optimize the local truncation errors of the main formulas for the block. The
method is zero-stable and consistent with sixth algebraic order. Some numerical examples are debated to demonstrate the efficiency and the accuracy
of the proposed method.
450
469
Bothayna S. H.
Kashkari
Department of Mathematics, Faculty of Science
University of Jeddah
Saudi Arabia
bskashkari@uj.edu.sa
Sadeem
Alqarni
Department of Mathematics, Faculty of Science
Department of Mathematics, Faculty of Science
King Abdulaziz University
Al-Baha University
Saudi Arabia
Saudi Arabia
saalqarni@bu.edu.sa
Two-step hybrid block method
third-order initial value problems
stability
consistent
Article.4.pdf
[
[1]
B. Abdulqadri, Y. S. Ibrahim, A. O. Adesanya, Hybrid one step block method for the solution of third order initial value problems of ordinary differential equations, Int. J. Appl. Math. Comput, 6 (2014), 10-16
##[2]
A. O. Adesanya, M. O. Udo, A. M. Alkali , A new block-predictor corrector algorithm for the solution of \(y''' = f(x, y, y', y'')\), American J. Comput. Math., 2 (2012), 341-344
##[3]
A. O. Adesanya, D. M. Udoh, A. Ajileye, A new hybrid block method for the solution of general third order initial value problems of ordinary differential equations, Int. J. Pure. Appl. Math., 86 (2013), 365-375
##[4]
T. A. Anake, D. O. Awoyemi, A. O. Adesanya , One-step implicit hybrid block method for the direct solution of general second order ordinary differential equations, IAENG Int. J. Appl. Math., 42 (2012), 224-228
##[5]
D. O. Awoyemi , A P-stable linear multistep method for solving general third order ordinary differential equations, Int. J. Comput. Math., 80 (2003), 987-993
##[6]
M. T. Chu, H. Hamilton, Parallel solution of ode’s by multiblock methods, SIAM J. Sci. Stat. Comput., 8 (1987), 342-353
##[7]
G. Dahlquist , Convergence and stability in the numerical integration of ordinary differential equations, Math. Scand., 4 (1956), 33-53
##[8]
K. M. Fasasi, New continuous hybrid constant block method for the solution of third order initial value problem of ordinary differential equations, Academic J. Appl. Math. Sci., 4 (2018), 53-60
##[9]
K. M. Fasasi, A. O. Adesanya, S. O. Adee, One step continuous hybrid block method for the solution of\( y''' = f(x, y, y', y'')\), J. Natural Sciences Research, 4 (2014), 55-62
##[10]
M. Hijazi, R. Abdelrahim, The numerical computation of three step hybrid block method for directly solving third order ordinary differential equations, Global J. Pure. Appl. Math., 13 (2017), 89-103
##[11]
Z. B. Ibrahim , Block multistep methods for solving ordinary differential equations, Ph.D. thesis, Universiti Putra Malaysia (2006)
##[12]
S. N. Jator, A sixth order linear multistep method for the direct solution of \(y'' = f(x, y, y')\), Int. J. Pure Appl. Math., 40 (2007), 457-472
##[13]
J. D. Lambert, I. A. Watson, Symmetric multistip methods for periodic initial value problems, IMA J. Appl. Math., 18 (1976), 189-202
##[14]
W. E. Milne, Numerical solution of differential equations, John Wiley & Sons, New York (1953)
##[15]
S. Ola Fatunla, Block methods for second order odes, Int. J. Comput. Math., 41 (1991), 55-63
##[16]
B. T. Olabode, Y. Yusuph, A new block method for special third order ordinary differential equations, J. Math. Stat., 5 (2009), 167-170
##[17]
Z. Omar, M. Sulaiman, Parallel r-point implicit block method for solving higher order ordinary differential equations directly, J. ICT, 3 (2004), 53-66
##[18]
H. Ramos, Z. Kalogiratou, T. Monovasilis, T. E. Simos, An optimized two-step hybrid block method for solving general second order initial-value problems, Numer. Algorithms, 72 (2016), 1089-1102
##[19]
L. F. Shampine, H. A. Watts, Block implicit one-step methods, Math. Comp., 23 (1969), 731-740
##[20]
L. K. Yap, F. Ismail, N. Senu, An accurate block hybrid collocation method for third order ordinary differential equations, J. Appl. Math., 2014 (2014), 1-9
]
A new generated distribution to analyze a practical engineering problem and applications
A new generated distribution to analyze a practical engineering problem and applications
en
en
There are many systems that can handle a mix of series-parallel or parallel-series systems. Here, a new three-parameter distribution motivated mainly by dealing with series-parallel or parallel-series systems is introduced. Moments, conditional moments, mean deviations, moment generating function, quantile, Lorenz, and Bonferroni curves of the new distribution including are presented. Entropy measures are given and estimation of its parameters is studied. Two real data applications are described to show its superior performance versus some known lifetime models.
470
484
Enayat M.
Abd Elrazik
Department of MIS, Yanbu
Taibah University
Saudi Arabia
ekhalilabdelgawad@taibahu.edu.sa
Mahmoud M.
Mansour
Department of Statistics, Mathematics and Insurance
Benha University
Egypt
mmmansour@taibahu.edu.sa
Lindley distribution
geometric distribution
maximum likelihood estimation
truncated Poisson distribution
Article.5.pdf
[
[1]
H. S. Bakouch, B. M. Al-Zahrani, A. A. Al-Shomrani, V. A. A. Marchi, F. Louzada , An extended Lindley distribution, J. Korean Statist. Soc., 41 (2012), 75-85
##[2]
T. Bjerkedal, Acquisition of Resistance in Guinea Pies infected with Different Doses of Virulent Tubercle, American J. Hygiene, 72 (1960), 130-148
##[3]
M. E. Ghitany, D. K. Al-Mutairi, S. Nadarajah , Zero-truncated Poisson-Lindley distribution and its Applications, Math. Comput. Simulation, 79 (2008), 279-287
##[4]
W. H. Gui, S. L. Zhang, X. M. Lu , The Lindley-Poisson distribution in lifetime analysis and its properties, Hacet. J. Math. Stat., 43 (2014), 1063-1077
##[5]
E. Mahmoudi, H. Zakerzadeh, Generalized poisson-lindley distribution, Comm. Statist. Theory Methods, 39 (2010), 1785-1798
##[6]
F. Merovci, Transmuted lindley distribution, Int. J. Open Prob. Comput. Sci. Math., 6 (2013), 63-72
##[7]
S. Nadarajah, H. S. Bakouch, R. Tahmasbi , A generalized Lindley distribution, Sankhya B, 73 (2011), 331-359
##[8]
S. Nadarajah, V. G. Cancho, E. M. M. Ortega , The geometric exponential Poisson distribution, Stat. Methods Appl., 22 (2013), 355-380
##[9]
A. Renyi , On measures of entropy and information, Proc. 4th Berkeley Sympos. Math. Statist. and Prob. (Univ. California Press, Berkeley), 1961 (1961 ), 547-561
##[10]
M. Sankaran, The discrete Poisson-Lindley distribution, Biometrics, 26 (1970), 145-149
##[11]
R. Shanker, S. Sharma, R. Shanker , A two-parameter Lindley distribution for modeling waiting and survival times data, Appl. Math., 4 (2013), 363-368
##[12]
C. E. Shannon, A Mathematical Theory of Communication, Bell System Tech. J., 27 (1948), 379-423
##[13]
H. Zakerzadah, A. Dolati, Generalized Lindley distribution , J. Math. Ext., 3 (2010), 13-25
##[14]
H. Zakerzadeh, E. Mahmoudi, A new two parameter lifetime distribution: model and properties, arXiv preprint, 2012 (2012), 1-19
]
On positive travelling wave solutions for a general class of KdV-Burger type equation
On positive travelling wave solutions for a general class of KdV-Burger type equation
en
en
In this paper, we establish the existence of positive traveling
waves solutions for the third order differential equation
\(u_{t}+\alpha u_{xx}+\beta u_{xxx}+\left(f\left(x,u(x)\right)\right)_{x}=0\),
where \(t,x\in\bf R\), \(f\) is a non-negative continuous function with some properties.
The result is a consequence of the characterization of the travelling wave
solutions as fixed points of some functional, defined using the Green's function
associated to the linear problem, and the Krasnosel'skii fixed point theorem on
cone expansion and compression of norm type.
485
502
Gilberto
Arenas-Díaz
Escuela de Matematicas
Universidad Industrial de Santander
Colombia
garenasd@uis.edu.co
José R.
Quintero
Departamento de Matematicas
Universidad del Valle
Colombia
jose.quintero@correounivalle.edu.co
Travelling wave solutions
Green function
Krasnosel'skii fixed point theorem
Article.6.pdf
[
]