Trend to spatial homogeneity for solutions to semilinear damped wave equations
Joan Solà-Morales, M. València · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1987
Synopsis The semilinear damped wave equations subject to homogeneous Neumann boundary conditions, admit spatially homogeneous solutions (i.e. u ( x , t ) = u ( t )). In order that every solution tends to a spatially homogeneous one, we look for conditions on the coefficients a and d , and on the Lipschitz constant of f with respect to u .