We study the time-periodic solutions to systems of conservation laws with ellipticity. It is shown that under time-periodic boundary condition, the system admits at least one global time-periodic solution bounded uniformly with the same period.

In this paper a nonliuear system of second order equations of mixed type is considered. The existence of H¹ strong solution for the modified Tricomi problem is proved by the energy integral method and the Leray-Schauder's fixed point principle.

This paper is concerned with asymptotic behavior, as time tends to infinity, of globally defined smooth (large) solutions to the system in one-dimensional nonlinear thermoviscoelasticity. Our results show that the global smooth solution approaches to the solution in the H¹ norm to the corresponding stationary problem, as time tends to infinity.

This paper deals with the global positive solutions of convective porous medium systems with nonlinear forcing at the boundary. Necessary and sufficient conditions on the global existence of all positive solutions are obtained.

The aim of this paper is to discuss the Cauchy problem for degenerate quasilinear hyperbolic equations of the form \frac{∂u}{∂t} + \frac{∂u^m}{∂x} = -u^p, m > 1, p > 0  with measures as initial conditions. The existence and uniqueness of solutions are obtained. In particular, we prove the following results: (1) 0 < p < 1 is a necessary and sufficient condition for the above equations to have extinction property; (2) 0 < p < m is a necessary and sufficient condition for the above equations to have localization property of the propagation of perturbations.

Support analysis is performed for solutions of nonlinear reaction-convection equations in which both singular flux and source term are included. The positivity versus instantaneous shrinking for the solutions is determined by the relative strength of the flux and the source, as well as the decay rate at infinity of initial value of solutions. As an application of the analysis, the case of power-type nonlinearities is checked in details.