JOURNAL OF DIFFERENTIAL EQUATIONS

dc.creatorQuaas-Berger, Alexander
dc.creatorRodríguez-Paredes, Andrei Enrique
dc.date2021-08-23T22:55:04Z
dc.date2022-07-07T02:30:52Z
dc.date2021-08-23T22:55:04Z
dc.date2022-07-07T02:30:52Z
dc.date2018
dc.date.accessioned2023-08-22T22:16:45Z
dc.date.available2023-08-22T22:16:45Z
dc.identifier1151180
dc.identifier1151180
dc.identifierhttps://hdl.handle.net/10533/251540
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/8346308
dc.descriptionWe study whether the solutions of a fully nonlinear, uniformly parabolic equation with superquadratic growth in the gradient satisfy initial and homogeneous boundary conditions in the classical sense, a problem we refer to as the classical Dirichlet problem. Our main results are: the nonexistence of global-in-time solutions of this problem, depending on a specific largeness condition on the initial data, and the existence of local-in-time solutions for initial data C-1 up to the boundary. Global existence is know when boundary conditions are understood in the viscosity sense, what is known as the generalized Dirichlet problem. Therefore, our result implies loss of boundary conditions in finite time. Specifically, a solution satisfying homogeneous boundary conditions in the viscosity sense eventually becomes strictly positive at some point of the boundary. (C) 2017 Elsevier Inc. All rights reserved.
dc.descriptionRegular 2015
dc.descriptionFONDECYT
dc.descriptionFONDECYT
dc.languageeng
dc.relationhandle/10533/111557
dc.relationhandle/10533/111541
dc.relationhandle/10533/108045
dc.relationhttps://doi.org/10.1016/j.jde.2017.11.008
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 Chile
dc.rightshttp://creativecommons.org/licenses/by-nc-nd/3.0/cl/
dc.rightsinfo:eu-repo/semantics/article
dc.rightsinfo:eu-repo/semantics/openAccess
dc.titleLoss of boundary conditions for fully nonlinear parabolic equations with superquadratic gradient terms
dc.titleJOURNAL OF DIFFERENTIAL EQUATIONS
dc.typeArticulo
dc.typeinfo:eu-repo/semantics/publishedVersion


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