Blow-up of solutions for a class of nonlinear pseudoparabolic equations with a memory term
type: Item
instance of: scholarly article
title: Blow-up of solutions for a class of nonlinear pseudoparabolic equations with a memory term
zbMATH Open document ID: 1470.35209
DOI: 10.1155/2014/507494
author: Huafei Di
author: Yadong Shang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We consider the nonlinear pseudoparabolic equation with a memory term \(u_t - \Delta u - \Delta u_t + \int_0^t \lambda \left(t - \tau\right) \Delta u \left(\tau\right) d \tau = \text{d} \text{i} \text{v} \left(\left|\nabla u\right|^{p - 2} u\right) + u^{1 + \alpha}\), \(x \in \Omega\), \(t > 0\), with an initial condition and Dirichlet boundary condition. Under negative initial energy and suitable conditions on \(p\), \(\alpha\), and the relaxation function \(\lambda(t)\), we prove a finite-time blow-up result by using the concavity method.
Mathematics Subject Classification ID: 35K70
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35K35
zbMATH DE Number: 7022510
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/507494
OpenAlex ID: W2120429093
Wikidata QID: Q59038903
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description: scientific article; zbMATH DE number 7022510