a Department of Mathematics, Graduate School of Science, Osaka University Osaka, Toyonaka, 560-0043, Japan b Instituto de Matemáticas, Universidad Nacional Autónoma de México, Campus Morelia, AP 61-3 (Xangari), Morelia, Mexico
Abstract:
We study asymptotics around the final states of solutions to the nonlinear Klein-Gordon equations with quadratic nonlinearities in two space dimensions , where . We prove that if the final states