Nonlinear Pseudoparabolic Equation Research Articles

Solution of nonlinear pseudoparabolic equations by semidiscretization in time

In the paper existence theorems for nonlinear pseudoparabolic initial-boundary value problems are proved. To this end there is used the method of semidiscretization in time, where the nonlinear time dependent problem is approximated by a sequence of linear elliptic problems. With assumption of local Lipschitz and Holder-Llpschitz conditions with respect to the nonlinearity there is proved the existence of a unique solution in a sufficiently small time interval and convergence of the approximates to the solution. Furthermore, somewhat weakening the assumptions, a compactness criterion yields convergence of a subsequence of approximates and existence of a solution.

On some nonlinear pseudo-parabolic equations

On some nonlinear pseudo-parabolic equations

Galerkin approximations to non-linear pseudo-parabolic partal differential equations

Galerkin approximations to non-linear pseudo-parabolic partal differential equations

Uniform Error Estimates for Difference Approximations to NonLinear Pseudo-Parabolic Partial Differential Equations

Two difference-approximation schemes to a nonlinear pseudo-parabolic equation are developed. Each of these schemes is stable and possesses a unique solution which can be obtained by an iterative procedure. By means of a discrete energy estimate, each approximation is shown to converge in the uniform norm to the exact solution with a determined rate. It has also been found that for a fixed lattice, the solution to each of two difference approximations to a certain parabolic problem can be obtained as the limit of a sequence of difference approximations to a pseudo-parabolic problem.