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Movement of hot spots on the exterior domain of a ball under the Dirichlet boundary condition. (English) Zbl 1152.35321

Summary: We consider the Cauchy-Dirichlet problem of the heat equation in the exterior domain of a ball, and study the movement of hot spots \(H(t)\) as \(t\to\infty\). In particular, we give a rate for the hot spots to run away from the boundary of the domain as \(t\to\infty\). Furthermore we give a sufficient condition for the hot spots to consist of only one point after a finite time.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35K05 Heat equation
35K20 Initial-boundary value problems for second-order parabolic equations
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