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Volume 29, Issue 1
Regularity of Viscous Solutions for a Degenerate Non-linear Cauchy Problem

Eric Hernández Sastoque, Christian Klingenberg, Leonardo Rendón & Juan C. Juajibioy

DOI: 10.4208/jpde.v29.n1.2

J. Part. Diff. Eq., 29 (2016), pp. 14-21.

Published online: 2016-03

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  • Abstract
We consider the Cauchy problem for a class of nonlinear degenerate parabolic equation with forcing. By using the vanishing viscosity method it is possible to construct a generalized solution. Moreover, this solution is a Lipschitz function on the spatial variable and Hölder continuous with exponent 1/2 on the temporal variable.
  • Keywords

Viscosity solution Hölder estimates Hölder continuity

  • AMS Subject Headings

35K65, 35D10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

eric.hernandez@unimagdalena.edu.co (Eric Hernández Sastoque)

klingenberg@mathematik.uni-wuerzburg.de (Christian Klingenberg)

lrendona@unal.eu.co (Leonardo Rendón)

jcjuajibioyo@unal.edu.co (Juan C. Juajibioy)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-29-14, author = {Sastoque , Eric HernándezKlingenberg , ChristianRendón , Leonardo and Juajibioy , Juan C.}, title = {Regularity of Viscous Solutions for a Degenerate Non-linear Cauchy Problem}, journal = {Journal of Partial Differential Equations}, year = {2016}, volume = {29}, number = {1}, pages = {14--21}, abstract = { We consider the Cauchy problem for a class of nonlinear degenerate parabolic equation with forcing. By using the vanishing viscosity method it is possible to construct a generalized solution. Moreover, this solution is a Lipschitz function on the spatial variable and Hölder continuous with exponent 1/2 on the temporal variable.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v29.n1.2}, url = {http://global-sci.org/intro/article_detail/jpde/5075.html} }
TY - JOUR T1 - Regularity of Viscous Solutions for a Degenerate Non-linear Cauchy Problem AU - Sastoque , Eric Hernández AU - Klingenberg , Christian AU - Rendón , Leonardo AU - Juajibioy , Juan C. JO - Journal of Partial Differential Equations VL - 1 SP - 14 EP - 21 PY - 2016 DA - 2016/03 SN - 29 DO - http://doi.org/10.4208/jpde.v29.n1.2 UR - https://global-sci.org/intro/article_detail/jpde/5075.html KW - Viscosity solution KW - Hölder estimates KW - Hölder continuity AB - We consider the Cauchy problem for a class of nonlinear degenerate parabolic equation with forcing. By using the vanishing viscosity method it is possible to construct a generalized solution. Moreover, this solution is a Lipschitz function on the spatial variable and Hölder continuous with exponent 1/2 on the temporal variable.
Sastoque , Eric HernándezKlingenberg , ChristianRendón , Leonardo and Juajibioy , Juan C.. (2016). Regularity of Viscous Solutions for a Degenerate Non-linear Cauchy Problem. Journal of Partial Differential Equations. 29 (1). 14-21. doi:10.4208/jpde.v29.n1.2
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