Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Entropy solutions for diffusion-convection equations with partial diffusivity


Authors: M. Escobedo, J. L. Vázquez and Enrike Zuazua
Journal: Trans. Amer. Math. Soc. 343 (1994), 829-842
MSC: Primary 35K65; Secondary 35K55, 35L65, 35L67, 76D99, 76R99
MathSciNet review: 1225573
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the Cauchy problem for the following scalar conservation law with partial viscosity

$\displaystyle {u_t} = {\Delta _x}u + {\partial _y}(f(u)),\quad (x,y) \in {{\mathbf{R}}^N},t > 0.$

The existence of solutions is proved by the vanishing viscosity method. By introducing a suitable entropy condition we prove uniqueness of solutions. This entropy condition is inspired by the entropy criterion introduced by Kruzhkov for hyperbolic conservation laws but it takes into account the effect of diffusion.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35K65, 35K55, 35L65, 35L67, 76D99, 76R99

Retrieve articles in all journals with MSC: 35K65, 35K55, 35L65, 35L67, 76D99, 76R99


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1225573-2
PII: S 0002-9947(1994)1225573-2
Keywords: Convection-diffusion equations, scalar conservation laws, partial diffusivity, entropy criterion, uniqueness, vanishing viscosity
Article copyright: © Copyright 1994 American Mathematical Society