On positive solutions of some periodic parabolic eigenvalue problem with a weight function
type: Item
instance of: scholarly article
title: On positive solutions of some periodic parabolic eigenvalue problem with a weight function
zbMATH Open document ID: 0937.35005
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1999-11-29T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108486
review text: Let \(\Omega\) be a bounded domain in \(\mathbb{R}^n\), and let \(m=m(x,t)\) be a \(T\)-periodic in \(t\) real function on \(\Omega\times \mathbb{R}\) whose restriction to \(\Omega\times (0, T)\) is in \(L^r(\Omega\times(0, T))\) for some \(r>n+2\). The paper finds necessary and sufficient conditions on \(m\) for the existence, uniqueness and simplicity of the principal eigenvalue for the following periodic weighted Dirichlet and Neumann parabolic eigenvalue problem \[ {\partial u\over\partial t}-\sum_{i,j}a_{i,j} {\partial^2 u\over\partial x_i\partial x_j}- \sum_j a_j{\partial u\over\partial x_j}= \lambda mu ,\quad B(u)=0 ,\quad u(x,t)=u(x,t+T) , \] where either \(B(u)=u|_{\partial\Omega\times R}\) (Dirichlet condition) or \(B(u)=(\partial u/\partial\nu)|_{\partial\Omega\times R}\) (Neumann condition).
reviewed by: Ivan Ginchev
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 1319588
zbMATH Keywords: existence, uniqueness and simplicity of the principal eigenvalue
author: T. Godoy
author: Alfredo Guerin
author: Sofia Paczka
MaRDI profile type: Publication
cites work: Q3915354
cites work: On the principal eigenvalue of a periodic-parabolic operator
cites work: Bifurcation, perturbation of simple eigenvalues, and linearized stability
cites work: The periodic parabolic eigenvalue problem with $L^\infty$ weight.
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cites work: Q4359748
cites work: Compact positive mappings in Lebesgue spaces
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description: scientific article; zbMATH DE number 1319588