“Co-properties” of the nonlinear semi-group on L∞ generated by a scalar conservation law with p–Laplacian viscosity

This paper concerns properties of solutions to the Cauchy problem of scalar conservation law with p–Laplacian viscosity. We firstly prove the existence and uniqueness of solution with L∞ initial data, and give uniform estimates of the solution and its derivative. Then, we use these estimates to prove that the semi-group on L∞, generated by the solution map, satisfies the properties of comparison, contraction, conservation and constants, which are called “Co-properties.” “Co-properties” can be used to study the large time stability of solutions to the equation.