Global Attractors for a Semilinear Hyperbolic Equation in Viscoelasticity
Copyright policy )Global Attractors for a Semilinear Hyperbolic Equation in Viscoelasticity
A semilinear partial differential equation of hyperbolic type with a convolution term describing simple viscoelastic materials with fading memory is considered. Regarding the past history (memory) of the displacement as a new variable, the equation is transformed into a dynamical system in a suitable Hilbert space. The dissipation is extremely weak, and it is all contained in the memory term. Longtime behavior of solutions is analyzed. In particular, in the autonomous case, the existence of a global attractor for solutions is achieved.
- University of Brescia Italy
- Polytechnic University of Milan Italy
Viscoelasticity; Memory kernel; Absorbing set; Global attractor, Applied Mathematics, global attractor, exponential decay, absorbing set, memory kernel, Attractors, Linear constitutive equations for materials with memory, viscoelasticity, viscoelastic materials with fading memory, Analysis, Second-order nonlinear hyperbolic equations
Viscoelasticity; Memory kernel; Absorbing set; Global attractor, Applied Mathematics, global attractor, exponential decay, absorbing set, memory kernel, Attractors, Linear constitutive equations for materials with memory, viscoelasticity, viscoelastic materials with fading memory, Analysis, Second-order nonlinear hyperbolic equations
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