Open AccessDamped Klein-Gordon equation with variable diffusion coefficient
Author(s) -
Qinghua Luo
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021139
Subject(s) - uniqueness , klein–gordon equation , variable coefficient , mathematics , variable (mathematics) , nonlinear system , mathematical analysis , diffusion equation , diffusion , set (abstract data type) , physics , computer science , thermodynamics , quantum mechanics , economy , economics , programming language , service (business)
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.