TY - JOUR

T1 - Hot spots for the heat equation with a rapidly decaying negative potential

AU - Ishige, K.

AU - Kabeya, Y.

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 2009

Y1 - 2009

N2 - We consider the Cauchy problem of the heat equation with a radially symmetric, negative potential -V which behaves like V (r) = O(r-k) as r → ∞, for some k > 2, and study the relation between the large-time behavior of hot spots of the solutions and the behavior of the potential at the space infinity. In particular, we prove that the hot spots tend to the space infinity as t → ∞ and how their rates depend on whether V ({norm of matrix} ̇ {norm of matrix}) ε L1(RN) or not.

AB - We consider the Cauchy problem of the heat equation with a radially symmetric, negative potential -V which behaves like V (r) = O(r-k) as r → ∞, for some k > 2, and study the relation between the large-time behavior of hot spots of the solutions and the behavior of the potential at the space infinity. In particular, we prove that the hot spots tend to the space infinity as t → ∞ and how their rates depend on whether V ({norm of matrix} ̇ {norm of matrix}) ε L1(RN) or not.

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M3 - Article

AN - SCOPUS:84856291660

VL - 14

SP - 643

EP - 662

JO - Advances in Differential Equations

JF - Advances in Differential Equations

SN - 1079-9389

IS - 7-8

ER -