Analytical-Numerical Study of Finite-Time Blow-up of the Solution to the Initial-Boundary Value Problem for the Nonlinear Klein–Gordon Equation

Abstract

An analytical-numerical approach is used to study the finite-time blow-up of the solution to the initial boundary-value problem for the nonlinear Klein–Gordon equation. An analytical analysis yields an upper estimate for the blow-up time of the solution with an arbitrary positive initial energy. With the use of this a priori information, the blow-up process is numerically analyzed in more detail. It is shown that the numerical analysis of the blow-up of the solution makes it possible to improve the analytical estimate and to detect local blow-up with respect to the spatial variable.