Method of lines for pseudoparabolic equations
Volume 120 / 2017
Annales Polonici Mathematici 120 (2017), 41-61
MSC: 35K70, 65M20, 35B44.
DOI: 10.4064/ap4097-9-2017
Published online: 9 November 2017
Abstract
We consider initial-boundary-value problems for a class of pseudoparabolic partial differential equations. Local-in-time existence results and nonexistence of global-in-time solutions are proved. We apply the method of lines to approximate pseudoparabolic equations by systems of ordinary differential equations. We present a complete convergence analysis for this semidiscretization method. Blow-up for approximate solutions is showed. Numerical experiments confirm the theoretical results.
