Blow-up and polynomial decay of solutions for a viscoelastic equation with a nonlinear source

DOI10.4171/ZAA/1458zbMath1250.74011MaRDI QIDQ713220

Yangping Xiong

Publication date: 26 October 2012

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

zbMATH Keywords

blow upviscoelasticpolynomially decay

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Integro-partial differential equations (45K05) Linear constitutive equations for materials with memory (74D05) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (2)

Growth of solutions with positive initial energy to systems of nonlinear wave equations with damping and source terms ⋮ Blow up of arbitrarily positive initial energy solutions for a viscoelastic wave equation

Cites Work

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• Global nonexistence for a quasilinear evolution equation with a generalized Lewis function
• Global nonexistence of solutions to a semilinear wave equation in the Minkowski space
• Global nonexistence for a semilinear Petrovsky equation
• Asymptotic behaviors of solutions for time dependent damped wave equations
• On a large class of kernels yielding exponential stability in viscoelasticity
• General decay of solutions of a viscoelastic equation
• A blow up result for a nonlinear wave equation with damping and vanishing initial energy in \(\mathbb R^N\)
• Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation
• Global existence and nonexistence for a nonlinear wave equation with damping and source terms

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