S. Kharibegashvili

Boundary Value Problems for Some Classes of Nonlinear Wave Equations

abstract:
For some classes of nonlinear wave equations, the boundary value problems (the first Darboux problem and their multi-dimensional versions, the characteristic Cauchy problem, and so on) are considered in angular and conic domains. Depending on the exponent of nonlinearity and the spatial dimension of equations, the issues of the global and local solvability as well as of the smoothness and uniqueness of solutions of these problems are studied.

Mathematics Subject Classification: 35L06, 35L20, 36L35, 35L75

Key words and phrases: Characteristic Cauchy problem, characteristic boundary value problems, Darboux problems, nonlinear wave equations, global and local solvability, blow-up of solutions