Quasilinear parabolic systems under nonlinear boundary conditions
The author proves existence and regularity results for abstract quasilinear parabolic systems of the form \[ (*)\quad \partial u/\partial t+A(t,u)u=f(t,u),\quad B(t,u)u=g(t,u),\quad u(s)=u_ 0\quad for\quad s<t\leq T. \] An important example for which his results are applicable is the case of elliptic operators \[ A(t,u)u:=-D_ j(a_{jk}(\cdot,t,u)D_ ku)+a_ j(\cdot,t,u)D_ ju. \] A great variety of problems in applications lead to a system of the form (*). The wide range of applications of the author's results emphasize the importance of this paper.
scientific article; zbMATH DE number 3960083
scientific article