The first boundary value problem for solutions of degenerate quasilinear parabolic equations (Q1820317)

Existence and uniqueness of nonnegative solutions are established for the n-dimensional degenerate quasilinear parabolic equation \[ \partial u/\partial t=\sum \partial /\partial x_ i(\nu (u)A_{ij}(x,t,u)\partial u/\partial x_ j)+\sum B_ i(x,t,u)\partial u/\partial x_ i+C(x,t,u)u, \] (x,t)\(\in \Omega \times [0,T]\), \(u(x,0)=u_ 0(x)\), \(x\in \Omega\), \(u(x,t)=\psi (s,t)\), (x,t)\(\in \partial \Omega \times [0,T]\), where s is the parameter of \(\partial \Omega\). The equation is a generalization of the porous medium equation \(u_ t=\Delta (u^ m)\), \(m>1\). The solutions are obtained in a certain weak sense. The results extend earlier results of the author to allow a more general class of coefficients.