Communications on Pure & Applied Analysis · 2005 · 88 citations · 15 references
Natural SciencesMathematicsPhysicsDifferential EquationsDynamical SystemsFluid DynamicsChaos TheoryDissipative SystemsHyperbolic DynamicsNonlinear DynamicsPartial Differential EquationsViscoelastic BehaviorAttractorsDissipationDissipative Dynamical SystemsDissipative DynamicsGlobal AttractorsHyperbolic AttractorsHyperbolic Partial Differential EquationsNonlinearity
We consider an integro-partialdifferential equation of hyperbolic typewith a cubic nonlinearity,in which no dissipation mechanism is present,except for the convolution term accounting forthe past memory of the variable.Setting the equation in the history space framework,we prove the existence of a regular global attractor.
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On the Strongly Damped Wave Equation
Vittorino Pata, Marco Squassina · Communications in Mathematical Physics · 2004 · 166 citations