Perturbation of parabolic equations with time-dependent linear
operators: convergence of linear processes and solutions
Perturbation of parabolic equations with time-dependent linear
operators: convergence of linear processes and solutions
In this work we consider parabolic equations of the form \[ (u_{\varepsilon})_t +A_{\varepsilon}(t)u_{{\varepsilon}} = F_{\varepsilon} (t,u_{{\varepsilon} }), \] where $\varepsilon$ is a parameter in $[0,\varepsilon_0)$ and $\{A_{\varepsilon}(t), \ t\in \mathbb{R}\}$ is a family of uniformly sectorial operators. As $\varepsilon \rightarrow 0^{+}$, we assume that the equation converges to \[ u_t …