The Cauchy problem for the Finsler heat equation

2017/10/02 by Akagi, Goro, Ishige, Kazuhiro, Sato, Ryuichi · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.00456

Abstract

Let H be a norm of \bf R^N and H₀ the dual norm of H. Denote by Δ_H the Finsler-Laplace operator defined by Δ_Hu:=div (H(∇ u)∇_ξH(∇ u)). In this paper we prove that the Finsler-Laplace operator Δ_H acts as a linear operator to H₀-radially symmetric smooth functions. Furthermore, we obtain an optimal sufficient condition for the existence of the solution to the Cauchy problem for the Finsler heat equation ∂_t u=Δ_H u, x∈\bf R^N, tgt;0, where N≥ 1 and ∂_t:=∂/∂ t.

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• Initial traces and solvability of the fast diffusion equation with power-type nonlinearity
• Initial traces and solvability of porous medium equation with power nonlinearity

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