Remarks on Radial Solutions of a Parabolic Gelfand-Type Equation

نویسندگان

چکیده

We consider an equation with exponential nonlinearity under the Dirichlet boundary condition. For a one- or two-dimensional domain, global solution has been obtained. In this paper, to extend result higher dimensional case, we concentrate on radial solutions in annulus. First, construct time-local abstract theory of differential equations. Next, show that decreasing energy exists problem. Finally, establish for sufficiently small initial value and parameter by Sobolev embedding Poincaré inequalities together some technical estimates. Moreover, when take smaller parameter, prove tends zero as time goes infinity.

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ژورنال

عنوان ژورنال: Axioms

سال: 2022

ISSN: ['2075-1680']

DOI: https://doi.org/10.3390/axioms11090429