On existence of solutions of mixed problems for parabolic systems (Q1327690)

Local and global existence results for quasilinear parabolic systems with nonlinear boundary conditions are established. Analogous results were proved before in \textit{J. Filo} and \textit{J. Kačur} [Comenius University Math. Preprint No. M5-91 (1991), to appear in Nonlinear Anal., Theor. Methods Appl.] for a right hand side that did not depend on the gradient of the solution. In the present paper a stronger monotonicity condition is assumed and the right hand side depends also on the gradient of the solution.