A semilinear reaction-diffusion system of equations and large diffusion
The author deals with the following semilinear system of reaction and diffusion equations \[ \left.\begin{aligned} \partial_t u-\text{Div}(D^\varepsilon \nabla u)+V^\varepsilon u+\lambda u=f(u)\qquad & \text{in }\Omega,\;t>0\\ \partial_nu+B^\varepsilon u=g(u)\qquad & \text{on }\Gamma\\ u(0)=u^\varepsilon_0\qquad & \text{in }\Omega\end{aligned}\right\}\tag{1} \] with nonlinear flux. The author studies the natural limit of the solutions (1) for large diffusivity. To this end, the author first shows the existence of a global attractor \({\mathcal A}^\varepsilon\) and proves that the flow on the family of attractors \({\mathcal A}^\varepsilon\) are essentially close to one generated by ODEs, which is a natural limit process for large diffusivity.
scientific article; zbMATH DE number 2128700
scientific article