On the profile of solutions with time-dependent singularities for the heat equation

Kodai Mathematical Journal

article

Toru Kan¹  Jin Takahashi¹ 

[1] Department of Mathematics Tokyo Institute of Technology

DOI  :  10.2996/kmj/1414674609

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

Let N ≥ 2, T ∈ (0,∞] and ξ ∈ C (0, T ; R N ). Under some regularity condition for ξ, it is known that the heat equation u t − Δ u = 0, x ∈ R N \ {ξ( t )}, t ∈ (0, T ) has a solution behaving like the fundamental solution of the Laplace equation as x → ξ( t ) for any fixed t . In this paper we construct a singular solution whose behavior near x = ξ( t ) suddenly changes from that of the fundamental solution of the Laplace equation at some t .

【 授权许可】

Unknown