Continuous dependence on the derivative of generalized heat equations

الأصل · EN

We consider here a generalized heat equation ∂ₜ ρ=d/dxd/dWρ, where W is a finite measure on the one dimensional torus, and d/dW is the Radon-Nikodym derivative with respect to W. Such equation has appeared in different contexts, 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 in proving, for a suitable topology, a continuous dependence of the solution ρ as a function of W.