Numerical Simulations on Two Nonlinear Biharmonic Evolution Equations
نویسنده
چکیده
We numerically simulate the following two nonlinear evolution equations with a fourth order (biharmonic) leading term: −∆2u− 1 22 (|u|2 − 1)u = ut in Ω ⊂ R or R and −∆2u + 1 22 ∇ · ((|∇u|2 − 1)∇u) = ut in Ω ⊂ R or R with an initial value and a Dirichlet boundary conditions. We use a bivariate spline space like finite element method to solve these equations. We discuss the convergence of our numerical scheme and present several numerical experiments under different boundary conditions and different domains in the bivariate setting. AMS 2000 Mathematics Subject Classifications: 35J35, 35K55, 65M12, 65M60
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تاریخ انتشار 1999