Global Attractors for a Semilinear Hyperbolic Equation in Viscoelasticity

✍ Scribed by Claudio Giorgi; Jaime E. Muñoz Rivera; Vittorino Pata

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 120 KB
• Volume: 260
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2001.7437

✦ Synopsis

A semilinear partial differential equation of hyperbolic type with a convolution term describing simple viscoelastic materials with fading memory is considered.

Ž . 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.