Averaging of equations of viscoelasticity with singularly oscillating external forces

10 Jul 2016 Chepyzhov Vladimir V. Conti Monica Pata Vittorino

Given $\rho\in[0,1]$, we consider for $\varepsilon\in(0,1]$ the nonautonomous viscoelastic equation with a singularly oscillating external force $$ \partial_{tt} u-\kappa(0)\Delta u - \int_0^\infty \kappa'(s)\Delta u(t-s) d s +f(u)=g_{0}(t)+\varepsilon ^{-\rho }g_{1}(t/\varepsilon ) $$ together with the {\it averaged} equation $$ \partial_{tt} u-\kappa(0)\Delta u - \int_0^\infty \kappa'(s)\Delta u(t-s) d s +f(u)=g_{0}(t). $$ Under suitable assumptions on the nonlinearity and on the external force, the related solution processes $S_\varepsilon(t,\tau)$ acting on the natural weak energy space ${\mathcal H}$ are shown to possess uniform attractors ${\mathcal A}^\varepsilon$... (read more)

PDF Abstract
No code implementations yet. Submit your code now

Categories


  • ANALYSIS OF PDES
  • DYNAMICAL SYSTEMS