Title

Damped Klein-Gordon equation with variable diffusion coefficient.

Authors

Luo, Qinghua

Abstract

We consider a damped Klein-Gordon equation with a variable diffusion coefficient. This problem is challenging because of the equation's unbounded nonlinearity. First, we study the nonlinearity's continuity properties. Then the existence and the uniqueness of the solutions is established. The main result is the continuity of the solution map on the set of admissible parameters. Its application to the parameter identification problem is considered.

Subjects

HEAT equation; PARAMETER identification; ADMISSIBLE sets; KLEIN-Gordon equation; EQUATIONS; DIFFUSION coefficients; CONTINUITY

Publication

Communications on Pure & Applied Analysis, 2021, Vol 20, Issue 11, p3959

ISSN

1534-0392

Publication type

Academic Journal

DOI

10.3934/cpaa.2021139