The existence of solution for a stochastic fourth-order parabolic equation

Volume 9, Issue 2, pp 589--602 http://dx.doi.org/10.22436/jnsa.009.02.23

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Authors

Changchun Liu - School of Mathematics, Jilin University, Changchun 130012, China. Jiaojiao Wang - School of Mathematics, Jilin University, Changchun 130012, China.

Abstract

The authors consider stochastic equations of the prototype \[du + ( \gamma D^4u - \gamma D^2f'(u) + D^2u - f'(u))dt - dw = 0;\] where \(\gamma>0\) is a constant and \(w\) is a \(Q\)-Wiener process in a probability space \(( \Omega;F; P)\). We establish the global existence and uniqueness of the solution for this prototype in one dimension space. The random attractor is also discussed.

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Keywords

• Random term
• stochastic fourth-order equation
• global existence.

MSC

•  35R60
•  35G30

References

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