Taiwanese Journal of Mathematics · 2006 · 42 citations · 17 references
Natural SciencesMathematicsDifferential EquationsDynamical SystemsBoundary ConditionsBoundary-value ProblemsDissipative SystemsExistence TheoryInitial Value ProblemsPartial Differential EquationsAsymptotic Boundary ConditionsAsymptotic TheoryBlow-up CriteriaBlow-up PhenomenaDampingGlobal Existence TheoryInitial-boundary Value ProblemsIntegrable Partial Differential Equations
The initial boundary value problem for an integro-differential equation with strong damping in a bounded domain is considered. The existence, asymptotic behavior and blow-up of solutions are discussed under some conditions. The decay estimates of the energy function and the estimates of the lifespan of blow-up solutions are given.
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