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 expL2(RN + ). Furthermore, we derive decay estimates and the asymptotic behavior for small global-in-time solutions.
Heat equation with an exponential nonlinear boundary condition in the half space / G. Furioli, T. Kawakami, E. Terraneo. - In: SN PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 2662-2963. - 3:3(2022), pp. 36.1-36.44. [10.1007/s42985-022-00170-7]
Heat equation with an exponential nonlinear boundary condition in the half space
E. TerraneoUltimo
2022
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 expL2(RN + ). Furthermore, we derive decay estimates and the asymptotic behavior for small global-in-time solutions.
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