Compactness results for time-dependent parabolic systems
This paper considers the relative compactness in \(C^ 2\) of the orbits of certain systems of nonlinear parabolic partial differential equations where the highest order spatial operator is time-dependent, uniformly elliptic and quasi-linear, and the lower order terms are just continuous. The approach is to first obtain estimates for the abstract problem \(u_ t+A(t)u=f(u)\), \(u(0)=u_ 0\), a problem to which the theory of Sobolevskij may be applied. These estimates are of some interest in themselves.
scientific article; zbMATH DE number 3975457
scientific article