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Exponential decay for a viscoelastic problem with a singular kernel. (English) Zbl 1169.74013

Summary: We consider a problem which arises in viscoelasticity. We prove exponential decay of solutions for the problem with a memory term involving a kernel which is singular at zero. This is established by introducing an appropriate Lyapunov-type functional and using the energy method.

MSC:

74D05 Linear constitutive equations for materials with memory
74H40 Long-time behavior of solutions for dynamical problems in solid mechanics
45K05 Integro-partial differential equations
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