Search

Let $G$ be a compact Lie group. In this article, we investigate the Cauchy problem for a nonlinear wave equation with the viscoelastic damping on $G$. More precisely, we investigate some $L^2$-estimates for the solution to the homogeneous nonlinear viscoelastic damped wave equation on $G$ utilizing the group Fourier transform on $G$. We also prove that there is no improvement of any decay rate for the norm $\|u(t,\,\cdot )\|_{L^2(G)}$ by further assuming the $L^1(G)$-regularity of initial data. Finally, using the noncommutative Fourier analysis on compact Lie groups, we prove a local in time existence result in the energy space $\mathcal {C}^1([0,\,T],\,H^1_{\mathcal {L}}(G)).$

This paper is devoted to the study of the local existence, uniqueness, regularity, and continuous dependence of solutions to a logistic equation with memory in the Bessel potential spaces.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups

A DIFFUSIVE LOGISTIC EQUATION WITH MEMORY IN BESSEL POTENTIAL SPACES

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups

A DIFFUSIVE LOGISTIC EQUATION WITH MEMORY IN BESSEL POTENTIAL SPACES