S. Kharibegashvili
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