Classical Solutions To 1-D Physical Models With Large Initial Data

In the study of physics and its application area, mostly, the practical problem can be reduced to the mathematical problem. As an important system in wave theory and fluid mechanics etc., the research on wave equation is one of hot topics in mathematics and provides theoretical support for physics.In this paper, we consider the classical solutions to two 1-D physical models with large initial data. Firstly, we consider the classical solutions to Cauchy problem for the model of two-layer flows, which appears in shallow water theory. Under the appropriate assumptions on initial data, we can obtain the necessary and sufficient conditions of the global existence of classical solutions. Secondly, it is well known that the damping term prevents the breaking of waves of small amplitude, while it need to be discussed for large data specifically. We consider the effect of damping term on the solutions to the autonomous wave equation with damping term. We can get the singularity result formed in finite time for some large initial data.