Perturbation quasi différentielle d'un semi-groupe régularisant dans une échelle d'espaces de Banach. (Quasi differential perturbation of a regularizing semigrop in a scale of Banach spaces)
The authors give a global existence and uniqueness result for the evolution equation \(u_ t+Au=F(u)\), \(u(0)=u_ 0\), where -A is the infinitesimal generator of a linear semigroup S(t) smoothing in a scale of Banach spaces \(B_{\rho}\) \((0\leq \rho <\infty)\) and F is a nonlinear quasi differential operator consistent with S(t). They show that for \(u_ 0\) small enough in \(B_ 0\) there is a unique solution of the equation such that u(t) remains bounded in \(B_{\alpha t}\), for some \(\alpha >0\). The authors apply this result to the motion of the interface of two liquids in porous medium.
motion of the interface of two liquids in porous medium
scientific article; zbMATH DE number 4067669
scientific article