Approximate Solution of Stochastic Partial Differential Equation with Random Neumann Boundary Condition

A. H. EL_Bassiouny^1, , W. W. Mohammed¹ and F. Eskander¹

¹Department of Mathematics, Faculty of Science, Mansoura University, Egypt

Cite this paper:
A. H. EL_Bassiouny, W. W. Mohammed and F. Eskander. Approximate Solution of Stochastic Partial Differential Equation with Random Neumann Boundary Condition. International Journal of Partial Differential Equations and Applications. 2015; 3(1):20-24. doi: 10.12691/ijpdea-3-1-4

Abstract

In this paper we approximate the solution of a parabolic nonlinear stochastic partial differential equation (SPDE) with cubic nonlinearity and with random Neumann boundary condition via a stochastic ordinary differential equation (SODE) which is a stochastic amplitude equation near a change of stability.

Keywords:
amplitude equations SPDEs random boundary conditions multiscale analysis Ginzburg-Landau equation.

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