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Exponential decay of non‐linear wave equation with a viscoelastic boundary condition
Author(s) -
Rivera Jaime E. Muñoz,
Andrade Doherty
Publication year - 2000
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/(sici)1099-1476(20000110)23:1<41::aid-mma102>3.0.co;2-b
Subject(s) - mathematics , resolvent , exponential decay , viscoelasticity , exponential growth , mathematical analysis , relaxation (psychology) , exponential function , wave equation , boundary (topology) , kernel (algebra) , function (biology) , dissipation , exponential stability , boundary value problem , physics , nonlinear system , pure mathematics , quantum mechanics , psychology , social psychology , evolutionary biology , biology , thermodynamics
We study in this paper the global existence and exponential decay of solutions of the non‐linear unidimensional wave equation with a viscoelastic boundary condition. We prove that the dissipation induced by the memory effect is strong enough to secure global estimates, which allow us to show existence of global smooth solution for small initial data. We also prove that the solution decays exponentially provided the resolvent kernel of the relaxation function, k decays exponentially. When k decays polynomially, the solution decays polynomially and with the same rate. Copyright © 2000 John Wiley & Sons, Ltd.