Gradient estimates for solutions of parabolic equations and systems
Hans Engler, Bernhard Kawohl, Stephan Luckhaus · Journal of Mathematical Analysis and Applications · 1990
1. STATEMENT OF THE PROBLEM Let 52 c R”, n > 2, be a bounded domain with smooth boundary r= &2. In this note we study scalar quasilinear parabolic differential equations u, = div,Y(g( IVul’) VU) +f(u) = 0, (1) u,-A,u+f(u)=O (2) and systems u, DA,u + f(u) = 0 (3) on Q x (0, co), with initial conditions u( ., 0) = u0 resp. u( ., 0) = u0 and homogeneous Dirichlet boundary conditions u,i-X(O,CO)‘O for (1) and (2) resp. (4) u1r.x (0.00) = 0 for (3). (5)