On Nonextendable Solutions and Blow-Ups of Solutions of Pseudoparabolic Equations with Coercive and Constant-Sign Nonlinearities: Analytical and Numerical Study

Abstract

The blow-up of solutions of two initial boundary-value problems different in the form of the equation’s nonlinearity is investigated. This leads to different approaches to the analytical proof of the blow-up of solutions, but a result about the blow-up of solutions is obtained in both cases. The analytical study is supplemented by numerical investigations, which make it possible to determine the time of the blow-up and its character in each particular case.