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January/February 2015 Continuous dependence on the derivative of generalized heat equations
Tertuliano Franco, Julián Haddad
Differential Integral Equations 28(1/2): 59-78 (January/February 2015).

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 $W$.

Citation

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Tertuliano Franco. Julián Haddad. "Continuous dependence on the derivative of generalized heat equations." Differential Integral Equations 28 (1/2) 59 - 78, January/February 2015.

Information

Published: January/February 2015
First available in Project Euclid: 11 December 2014

zbMATH: 1349.35150
MathSciNet: MR3299117

Subjects:
Primary: 35K10 , 35K20

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 1/2 • January/February 2015
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