Entropy solutions for diffusion-convection equations with partial diffusivity
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- by M. Escobedo, J. L. Vázquez and Enrike Zuazua PDF
- Trans. Amer. Math. Soc. 343 (1994), 829-842 Request permission
Abstract:
We consider the Cauchy problem for the following scalar conservation law with partial viscosity \[ {u_t} = {\Delta _x}u + {\partial _y}(f(u)),\quad (x,y) \in {{\mathbf {R}}^N},t > 0.\] 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
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 343 (1994), 829-842
- MSC: Primary 35K65; Secondary 35K55, 35L65, 35L67, 76D99, 76R99
- DOI: https://doi.org/10.1090/S0002-9947-1994-1225573-2
- MathSciNet review: 1225573