On generalized damped Klein-Gordon equation with nonlinear memory
Khaldi Said, Menad Mohamed
TL;DR
This paper investigates how nonlinear memory affects the decay behavior and the range of exponents for solutions to a generalized damped Klein-Gordon equation, providing insights into the equation's long-term dynamics.
Contribution
It introduces a study of the nonlinear memory term's impact on decay estimates and admissible exponents in the generalized Klein-Gordon equation.
Findings
Decay estimates are affected by the nonlinear memory term.
The admissible range of the exponent p is characterized.
Conditions for global existence of solutions are established.
Abstract
In this paper we consider the Cauchy problem for linear dissipative generalized Klein-Gordon equations with nonlinear memory in the right hand side. Our goal is to study the effect of this nonlinearity on both the decay estimates of global solutions as well as the admissible range of the exponent p.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Stability and Controllability of Differential Equations · advanced mathematical theories