Bounded solutions of functional integro-differential equations arising from heat conduction in materials with memory. (English. Russian original) Zbl 1533.45005
J. Math. Sci., New York 276, No. 2, 237-252 (2023); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 178, 41-56 (2020).
Summary: In this paper, we consider recurrent behavior of bounded solutions for a functional integro-differential equation arising from heat conduction in materials with memory. Prior to the main results, we give a new version of composite theorem on measure pseudo almost automorphic functions involved in delay. Based on recently obtained results on the uniform exponential stability as well as contraction mapping principle, we prove some existence and uniqueness theorems on the recurrence of bounded mild solutions for the addressed equations with infinite delay. Finally, we finish this paper with an example on partial integro-differential equation which frequently comes to light in the study of heat conduction.
MSC:
| 45K05 | Integro-partial differential equations |
| 43A60 | Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions |
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
| 80A21 | Radiative heat transfer |
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