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Pseudo almost periodic solutions to integro-differential equations of heat conduction in materials with memory. (English) Zbl 1253.35195

Summary: We investigate the existence of pseudo almost periodic solutions for a class of integro-differential equation with nonlocal initial conditions arising in the study of heat conduction in materials with memory. We first establish some existence theorems for abstract semilinear integro-differential equations with nonlocal initial conditions, and then, we apply our abstract results to the addressed integro-differential equation arising in the study of heat conduction in materials with memory.

MSC:

35R09 Integro-partial differential equations
35B10 Periodic solutions to PDEs
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
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