Título :	Blow-up and bounded solutions for a semilinear parabolic problem in a saturable medium
Autor :	Fernandes, Juliana Maia, Liliane de Almeida
Assunto::	Equação parabólica Explosão em tempo infinito Variedade de Nehari
Fecha de publicación :	ago-2020
Editorial :	American Institute of Mathematical Sciences
Citación :	FERNANDES, Juliana; MAIA, Liliane. Blow-up and bounded solutions for a semilinear parabolic problem in a saturable medium. Discrete & Continuous Dynamical Systems, v. 41, n. 3, p. 1297-1318, mar. 2021. DOI: 10.3934/dcds.2020318.
Abstract:	The present paper is on the existence and behaviour of solutions for a class of semilinear parabolic equations, defined on a bounded smooth domain and assuming a nonlinearity asymptotically linear at infinity. The behavior of the solutions when the initial data varies in the phase space is analyzed. Global solutions are obtained, which may be bounded or blow-up in infinite time (grow-up). The main tools are the comparison principle and variational methods. In particular, the Nehari manifold is used to separate the phase space into regions of initial data where uniform boundedness or grow-up behavior of the semiflow may occur. Additionally, some attention is paid to initial data at high energy level.
DOI:	10.3934/dcds.2020318
metadata.dc.relation.publisherversion:	https://www.aimsciences.org/article/doi/10.3934/dcds.2020318
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