## Differential and Integral Equations

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

### Continuous dependence on the derivative of generalized heat equations

Tertuliano Franco and Julián Haddad

#### 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