Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 72, pp. 1-12.
Title: Solvability of characteristic boundary-value problems for
nonlinear equations with iterated wave operator in the
principal part
Authors: Sergo Kharibegashvili (A. Razmadze Math. Institute, Georgia)
Bidzina Midodashvili (A. Razmadze Math. Institute, Georgia)
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.
Submitted February 18, 2008. Published May 15, 2008.
Math Subject Classifications: 35L05, 35L35, 35L75.
Key Words: Characteristic boundary-value problem;
hyperbolic equations; wave operator;
power nonlinearity; nonexistence.