Satoshi Masaki, Jun-ichi Segata
Published 2017-03-15Version 1
In this paper, we consider the final state problem for the nonlinear Klein-Gordon equation (NLKG) with a critical nonlinearity in three space dimensions. We prove that for a given asymptotic profile, there exists a solution to (NLKG) which converges to given asymptotic profile as t to infinity. Here the asymptotic profile is given by the leading term of the solution to the linear Klein-Gordon equation with a logarithmic phase correction. Construction of a suitable approximate solution is based on the combination of Fourier series expansion for the nonlinearity used in our previous paper and smooth modification of phase correction by Ginibre-Ozawa.
Modified scattering for the quadratic nonlinear Klein-Gordon equation in two dimensions
Asymptotic profiles for the Cauchy problem of damped beam equation with two variable coefficients and derivative nonlinearity
Some remarks on the asymptotic profile of solutions to structurally damped $σ$-evolution equations
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