Heat equation with an exponential nonlinear boundary condition in the half space

Giulia Furioli (), Tatsuki Kawakami () and Elide Terraneo ()
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Giulia Furioli: DIGIP, Università di Bergamo
Tatsuki Kawakami: Ryukoku University
Elide Terraneo: Università degli Studi di Milano

Partial Differential Equations and Applications, 2022, vol. 3, issue 3, 1-44

Abstract: Abstract We consider the initial-boundary value problem for the heat equation in the half space with an exponential nonlinear boundary condition. We prove the existence of global-in-time solutions under the smallness condition on the initial data in the Orlicz space $$\mathrm {exp}L^2({\mathbb {R}}^N_+)$$ exp L 2 ( R + N ) . Furthermore, we derive decay estimates and the asymptotic behavior for small global-in-time solutions.

Keywords: Global existence; Asymptotic behavior; Initial-boundary value problem; Nonlinear boundary condition; Exponential nonlinearity; Orlicz space; 35A01; 35B40; 35K20; 35K60; 46E30 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00170-7

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