Existence and uniqueness for solutions of parabolic quasi-variational inequalities with impulse control and nonlinear source terms

Volume 9, Issue 2, pp 568--583 http://dx.doi.org/10.22436/jnsa.009.02.21

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Authors

Salah Boulaaras - Department Of Mathematics, College Of Sciences and Arts, Al-Qassim University, Al-Ras, Kingdom Of Saudi Arabia. - Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1, Ahmed Benbella, Algeria.

Abstract

In this paper, we present a new proof for the existence and uniqueness of solutions of parabolic quasivariational inequalities with impulse control. We prove some properties of the presented algorithm (see [S. Boulaaras, M. Haiour, Appl. Math. Comput., 217 (2011), 6443-6450], [S. Boulaaras, M. Haiour, Indaga. Math., 24 (2013), 161-173]) using a semi-implicit scheme with respect to the t-variable combined with a finite element spatial approximation.

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Keywords

• Parabolic quasi-variational inequality
• finite elements
• semi-implicit scheme
• contraction
• fixed point
• impulse control problem.

MSC

•  65M60
•  34A37
•  65K15
•  49J40
•  49M25

References

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