The non-existence of the nonnegative renormalized solutions for the systems of the quasilinear elliptic equations with the Dirichlet boundary-value conditions is showed,in terms of the comparison principle and the proof by contradiction.

Stability of renormalized solutions to a double degenerate parabolic equation

The existence of the renormalized solutions for the initial-boundary value problem of parabolic equation with small measure is established.

The existence and uniqueness of renormalized solutions of a doubly degenerate parabolic equation are discussed by means of parabolic regularization method.

Structure of global weak entropy solution for initial-boundary value problems of scalar conservation laws with non-convexity conditions;

Structure of the global weak entropy solution of nonconvex scalar conservation laws with boundary conditions;

By the polygonal approximation method,a global approximation solution is constructed for the initial-boundary value problem of nonconvex scalar conservation laws with two-side boundary effect,and its convergence to the global weak entropy solution of the corresponding problem is proved.

The renormalized series solutions are obtained by a projection and iteration method.