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.

This thesis is concerned with the global continuous weak entropy solution and the L~1 convergence rate of its viscosity approximations for the initial-boundary problem of scalar conservation laws.

A sufficient condition that its global continuous weak entropy solution exists and is unique for the initial-boundary problem of scalar convex conservation laws is given,and the global continuous weak entropy solution is constructed by the truncation method,as well as its boundary behaviors is obtained.

According to the structure of the global continuous weak entropy solution of the initial-boundary problem of scalar conservation laws, and using L1-stability lemma for nonhomogeneous viscous equations with initial-boundary conditions, This thesis attain a convergence rate that the viscosity solution converge to the inviscid solution in L1-norm.

Existence of global weak solutions to the semiconductor equations with heat effect;

Using the Galerkin method,the existence of a global weak solution was proven,indicating the solvability of the system and the possibility of numerical solutions.

The Galerkin method,together with the potential well(stable set) method,is employed to solve the existence of global weak solutions of the primary limit value of a kind of semi-linear parabolic equations: in case of high dimension when.