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 expL*2(R^N_+). Furthermore, we derive decay estimates and the asymptotic behavior for small global-in-time solutions.
(2022). Heat equation with an exponential nonlinear boundary condition in the half space [journal article - articolo]. In SN PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS. Retrieved from https://hdl.handle.net/10446/235890
Heat equation with an exponential nonlinear boundary condition in the half space
Furioli, Giulia;
2022-01-01
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 expL*2(R^N_+). Furthermore, we derive decay estimates and the asymptotic behavior for small global-in-time solutions.File allegato/i alla scheda:
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