Asymptotic Behavior of Solutions to Wave Equations with a Memory Condition at the Boundary
Santos, Mauro de Lima
Southwest Texas State University, Department of Mathematics
In this paper, we study the stability of solutions for wave equations whose boundary condition includes a integral that represents the memory effect. We show that the dissipation is strong enough to produce exponential decay of the solution, provided the relaxation function also decays exponentially. When the relaxation function decays polynomially, we show that the solution decays polynomially and with the same rate.
Wave equations, Asymptotic behavior
Santos, M. L. (2001). Asymptotic behavior of solutions to wave equations with a memory condition at the boundary. <i>Electronic Journal of Differential Equations, 2001</i>(73), pp. 1-11.
Attribution 4.0 International