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Global existence and nonexistence of solutions for a viscoelastic wave equation with nonlinear boundary source term
Author(s) -
Di Huafei,
Shang Yadong,
Peng Xiaoming
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500169
Subject(s) - mathematics , term (time) , nonlinear system , viscoelasticity , boundary value problem , relaxation (psychology) , mathematical analysis , wave equation , function (biology) , boundary (topology) , initial value problem , physics , psychology , social psychology , quantum mechanics , evolutionary biology , biology , thermodynamics
In this paper, we consider the initial boundary value problem for a viscoelastic wave equation with nonlinear boundary source term. First of all, we introduce a family of potential wells and prove the invariance of some sets. Then we establish the existence and nonexistence of global weak solution with small initial energy under suitable assumptions on the relaxation function g ( · ) , nonlinear function f ( · ) , the initial data and the parameters in the equation. Furthermore, we obtain the global existence of weak solution for the problem with critical initial conditions I ( u 0 ) ≥ 0 and E ( 0 ) = d .