12. Continuous dependence on the coefficients for a class of non-autonomous evolutionary equations
Marcus Waurick · 2019
The continuous dependence of solutions to certain equations on the coefficients is addressed. The class of equations under consideration has only recently be shown to be well posed. We give criteria that guarantee that convergence of the coefficients in the weak operator topology implies weak convergence of the respective solutions. We discuss three examples: A homogenization problem for a Kelvin-Voigt model for elasticity, the discussion of continuous dependence of the coefficients for acoustic waves with impedance type boundary conditions and a singular perturbation problem for a mixed type equation. By means of counterexamples, we show optimality of the results obtained.