TY - JOUR
T1 - Solving convection-diffusion equations with mixed, Neumann and Fourier boundary conditions and measures as data, by a duality method
AU - Droniou, Jérôme
PY - 2000/12/1
Y1 - 2000/12/1
N2 - In this paper, we prove, following [1], existence and uniqueness of the solutions of convection-diffusion equations on an open subset of ℝN, 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 (W1,q(Ω))&vprime;, 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.
AB - In this paper, we prove, following [1], existence and uniqueness of the solutions of convection-diffusion equations on an open subset of ℝN, 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 (W1,q(Ω))&vprime;, 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.
UR - http://www.scopus.com/inward/record.url?scp=0141599008&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0141599008
SN - 1079-9389
VL - 5
SP - 1341
EP - 1396
JO - Advances in Differential Equations
JF - Advances in Differential Equations
IS - 10-12
ER -