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The global solvability and asymptotic behavior of a transmission problem for Kirchhoff‐type wave equations with memory source on the boundary
Author(s) -
Liu Zhiqing,
Fang Zhong Bo
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5722
Subject(s) - mathematics , mathematical analysis , perturbation (astronomy) , energy method , type (biology) , transmission (telecommunications) , boundary value problem , boundary (topology) , wave equation , physics , ecology , quantum mechanics , biology , electrical engineering , engineering
A transmission problem for Kirchhoff‐type wave equations with memory source term on one part of the boundary feedback is considered. By using the Faedo‐Galerkin approximation technique, the method of Lyapunov functional and the energy perturbation technique, we establish well‐posedness of global solution and derive a general decay estimate of the energy.