Singular Perturbations of Forward-Backward p-Parabolic Equations
- 56 Downloads
In this paper we have proved the existence of entropy measure-valued solutions to forward-backward p-parabolic equations. We have obtained these solutions as singular limits of weak solutions to (p,q)-elliptic regularized boundary-value problems as ε → 0+. When q > 1 and q = 2 we have not defined yet admissible initial and final conditions even in the form of integral inequalities.
2010 Mathematics Subject ClassificationPrimary: 35D99, 35K55, 35K65, 35K92 Secondary: 28A33, 35B50, 35R25
Key words and phrasesentropy solution forward-backward parabolic equation gradient Young measure maximum principle
Unable to display preview. Download preview PDF.
- S.N. Antontsev, I.V. Kuznetsov, Existence of entropy measure-valued solutions for forward-backward p-parabolic equations, submitted to Siberian Electronic Mathematical Reports (SEMR).Google Scholar
- M. Borsuk, V. Kondratiev: Elliptic boundary value problems of second order in piecewise smooth domains, North-Holland Mathematical Library, 69, Elsevier, Amsterdam, 2006.Google Scholar
- D. Kinderlehrer, P. Pedregal, Gradient Young measures generated by sequences in Sobolev spaces, The Journal of Geometric Analysis 4, (1994), 59–90Google Scholar
- O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier, F. Lenzen: Variational methods in imaging, Applied Mathematical Sciences, 167, Springer, New York, 2009.Google Scholar