Asymptotic behaviors of solutions to a reaction–diffusion equation with isochronous nonlinearity - Amy Poh, Ai Ling; Shimojo, Masahiko (Journal of mathematical analysis and applications, 2018)
We study the initial boundary value problem for the reaction–diffusion equation with isochronous nonlinearity. We prove that small solutions become spatially homogeneous and is subject to the ODE part asymptotically. We also discuss blow-up of an parabolic system with quadratic nonlinearity having the origin as an uniform isochronous center.