Solving convection-diffusion equations with mixed, Neumann and Fourier boundary conditions and measures as data, by a duality method

Jérôme Droniou

Abstract

In this paper, we prove, following [1], existence and uniqueness of the solutions of convection-diffusion equations on an open subset of $\mathbb R^N$, with a measure as data and different boundary conditions: mixed, Neumann or Fourier. The first part is devoted to the proof of regularity results for solutions of convection-diffusion equations with these boundary conditions and data in $(W^{1,q}(\Omega))'$, when $q <N/(N-1)$. The second part transforms, thanks to a duality trick, these regularity results into existence and uniqueness results when the data are measures.

Article information

Source
Adv. Differential Equations, Volume 5, Number 10-12 (2000), 1341-1396.

Dates
First available in Project Euclid: 27 December 2012

Mathematical Reviews number (MathSciNet)
MR1785678

Zentralblatt MATH identifier
1213.35204

Subjects
Primary: 35J55
Secondary: 35D05 35D10 35R05: Partial differential equations with discontinuous coefficients or data

Citation

Droniou, Jérôme. Solving convection-diffusion equations with mixed, Neumann and Fourier boundary conditions and measures as data, by a duality method. Adv. Differential Equations 5 (2000), no. 10-12, 1341--1396. https://projecteuclid.org/euclid.ade/1356651226