Energy decay rate for a quasi-linear wave equation with localized strong dissipation
The purpose of this paper is to derive a sharp energy decay estimate for a quasi-linear wave equation with localized strong dissipation of the type ???(a(x)?ut) ? ? ? ( a ( x ) ? u t ) in a domain ? ? of RN R N , where a(x) a ( x ) is a nonnegative function supported only on a part of the boundary ?? ? ? . We note that the index of algebraic decay depends on dimension N N and no geometrical condition is imposed on the boundary ?? ? ? .
energy decay quasi-linear wave equation localized strong dissipation