Nonlinear partial differential equations

Nonlinear partial differential equations are mainly considered. While Newton's equation of motion is a differential equation for time-variable, partial differential equations have variables on time and space, by which they describe many phenomena in nature with mutual interactions expressed by nonlinear terms. With the nonlinear terms in partial differential equations, existence of solutions in global time and blowing-up in finite time are not trivial, and they are significant targets in mathematical analysis. In this analysis, the use and discovery of methods in real analysis, harmonic analysis, functional analysis, function space theory are required. That is why the theory on nonlinear partial differential equation is one of main topics in analysis. There is a background motivation that we are eager to expect a phenomenon in future from the observed phenomenon at the present time.