Arthur Cavalcante Cunha

Universidade Federal da Bahia, Brazil

Title: Uniform attractors for a nonautonomous semilinear evolution equation of second order

Abstract: We investigate the forward dynamics of a nonautonomous semilinear wave-type evolution problem, which models propagation phenomena in nonlinear elastic rods and ion-acoustic waves. We establish global well-posedness and prove the existence of a family of uniform attractors under appropriate growth and dissipativity conditions. Additionally, we demonstrate upper-semicontinuity in a suitable space and derive regularity results in a more refined space. Finally, we characterize the uniform attractor through kernel sections for the problem under consideration. PDF