Translator Disclaimer
2018 The heat equation for local Dirichlet forms: Existence and blow up of nonnegative solutions
Tarek Kenzizi
Rocky Mountain J. Math. 48(8): 2573-2593 (2018). DOI: 10.1216/RMJ-2018-48-8-2573

Abstract

We establish conditions ensuring either existence or blow up of nonnegative solutions for the following parabolic problem: \begin{equation} \begin{cases} Hu -Vu + ({\partial u}/{\partial t}) =0 & \mbox {in } X\times (0,T), \\ u(x,0)=u_{0}(x) & \mbox {in } X, \end{cases} \end{equation} where $T>0$, $X$ is a locally compact separable metric space, $H$ is a selfadjoint operator associated with a regular Dirichlet form $\mathcal E$; the initial value $u_{0}\in L^{2}(X,m)$, where $m$ is a positive Radon measure on Borel subset $U$ of $X$ such that $m(U)>0$ and $V$ is a Borel locally integrable function on $X$.

Citation

Download Citation

Tarek Kenzizi. "The heat equation for local Dirichlet forms: Existence and blow up of nonnegative solutions." Rocky Mountain J. Math. 48 (8) 2573 - 2593, 2018. https://doi.org/10.1216/RMJ-2018-48-8-2573

Information

Published: 2018
First available in Project Euclid: 30 December 2018

zbMATH: 1403.35120
MathSciNet: MR3894994
Digital Object Identifier: 10.1216/RMJ-2018-48-8-2573

Subjects:
Primary: 34B27, 35K08, 35K55

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
21 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.48 • No. 8 • 2018
Back to Top