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math.AP2021
Optimal well-posedness and forward self-similar solution for the Hardy-Hénon parabolic equation in critical weighted Lebesgue spaces
Noboru Chikami, Masahiro Ikeda, Koichi Taniguchi
The Cauchy problem for the Hardy-Hénon parabolic equation is studied in the critical and subcritical regime in weighted Lebesgue spaces on the Euclidean space . Well-…
math.AP2019
Global well-posedness, dissipation and blow up for semilinear heat equations in energy spaces associated with self-adjoint operators
Masahiro Ikeda, Koichi Taniguchi
The purpose in this paper is to determine the global behavior of solutions to the initial-boundary value problems for energy-subcritical and critical semilinear heat equations by i…
math.AP2017★ 2 cited
Gradient estimates and their optimality for heat equation in an exterior domain
Vladimir Georgiev, Koichi Taniguchi
This paper is devoted to the study of gradient estimates for the Dirichlet problem of the heat equation in the exterior domain of a compact set. Our results describe the time decay…