Solvability of characteristic boundary-value problems for nonlinear equations with iterated wave operator in the principal part

Abstract

A characteristic boundary-value problem for a hyperbolic equation with power nonlinearity and iterated wave operator in the principal part is considered in a conical domain. Depending on the exponent of nonlinearity and spatial dimensionality of the equation, the existence and uniqueness of the solution of a boundary-value problem is established. The non-solvability of this problem is also considered here.

Keywords

• Characteristic boundary-value problem
• hyperbolic equations
• wave operator
• power nonlinearity
• nonexistence