Differential and Integral Equations

Continuous dependence on the derivative of generalized heat equations

Tertuliano Franco and Julián Haddad

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Here, we consider a generalized heat equation $\partial_t \rho=\frac{d}{dx}\frac{d}{dW}\rho$, where $W$ is a finite measure on the one dimensional torus, and $\frac{d}{dW}$ is the Radon-Nikodym derivative with respect to $W$. Such an equation has appeared in different contexts, one of which being related to physical systems and representing a large class of classical and non-classical parabolic equations. As a natural assumption on $W$, we require that the Lebesgue measure is absolutely continuous with respect to $W$. The main result here presented consists of proving, for a suitable topology, a continuous dependence of the solution $\rho$ as a function of $W$.

Article information

Source
Differential Integral Equations, Volume 28, Number 1/2 (2015), 59-78.

Dates
First available in Project Euclid: 11 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1418310421

Mathematical Reviews number (MathSciNet)
MR3299117

Zentralblatt MATH identifier
1349.35150

Subjects
Primary: 35K10: Second-order parabolic equations 35K20: Initial-boundary value problems for second-order parabolic equations

Citation

Franco, Tertuliano; Haddad, Julián. Continuous dependence on the derivative of generalized heat equations. Differential Integral Equations 28 (2015), no. 1/2, 59--78. https://projecteuclid.org/euclid.die/1418310421


Export citation