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Method of lines for pseudoparabolic equations

Volume 120 / 2017

Danuta Jaruszewska-Walczak, Krzysztof A. Topolski 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.

Authors

  • Danuta Jaruszewska-WalczakInstitute of Mathematics
    Faculty of Mathematics, Physics and Informatics
    University of Gdańsk
    80-308 Gdańsk, Poland
    e-mail
  • Krzysztof A. TopolskiInstitute of Mathematics
    Faculty of Mathematics, Physics and Informatics
    University of Gdańsk
    80-308 Gdańsk, Poland
    e-mail

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