Attractors of nonlinear elliptic equations with a small parameter
The author studies the behavior of solutions to the equation \[ \varepsilon ^2u_{tt}(x,t)-2bu_t(x,t)+\triangle u(x,t)-f(u,t)=g(x,t),\quad x\in \Omega,\;t>0 \] satisfying data \(u=0\) on \(\partial \Omega , u(x,0)=u_0\) for \(\varepsilon \rightarrow 0.\) He proves upper semicontinuity of trajectory attractors in appropriate spaces.
scientific article; zbMATH DE number 1915935