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Existence and uniqueness of entropy solutions to strongly degenerate parabolic equations with discontinuous coefficients
1.  Department of General Education, Salesian Polytechnic, 468 Oyamagaoka, Machidacity, Tokyo, 1940215 
In particular, we consider the case that coefficients are the functions of bounded variation with respect to the space variable $x$. Then, we prove the existence of Kružkov type entropy solutions. Moreover, we prove the uniqueness of the solution under additional conditions.
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References:
[1] 
Hiroshi Watanabe. Solvability of boundary value problems for strongly degenerate parabolic equations with discontinuous coefficients. Discrete & Continuous Dynamical Systems  S, 2014, 7 (1) : 177189. doi: 10.3934/dcdss.2014.7.177 
[2] 
Sébastien Gouëzel. An interval map with a spectral gap on Lipschitz functions, but not on bounded variation functions. Discrete & Continuous Dynamical Systems  A, 2009, 24 (4) : 12051208. doi: 10.3934/dcds.2009.24.1205 
[3] 
Yunho Kim, Luminita A. Vese. Image recovery using functions of bounded variation and Sobolev spaces of negative differentiability. Inverse Problems & Imaging, 2009, 3 (1) : 4368. doi: 10.3934/ipi.2009.3.43 
[4] 
Pierpaolo Soravia. Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients. Communications on Pure & Applied Analysis, 2006, 5 (1) : 213240. doi: 10.3934/cpaa.2006.5.213 
[5] 
Dung Le. Partial regularity of solutions to a class of strongly coupled degenerate parabolic systems. Conference Publications, 2005, 2005 (Special) : 576586. doi: 10.3934/proc.2005.2005.576 
[6] 
Kenneth Hvistendahl Karlsen, Nils Henrik Risebro. On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients. Discrete & Continuous Dynamical Systems  A, 2003, 9 (5) : 10811104. doi: 10.3934/dcds.2003.9.1081 
[7] 
Denis R. Akhmetov, Renato Spigler. $L^1$estimates for the higherorder derivatives of solutions to parabolic equations subject to initial values of bounded total variation. Communications on Pure & Applied Analysis, 2007, 6 (4) : 10511074. doi: 10.3934/cpaa.2007.6.1051 
[8] 
GuiQiang Chen, Kenneth Hvistendahl Karlsen. Quasilinear anisotropic degenerate parabolic equations with timespace dependent diffusion coefficients. Communications on Pure & Applied Analysis, 2005, 4 (2) : 241266. doi: 10.3934/cpaa.2005.4.241 
[9] 
Zhigang Wang, Lei Wang, Yachun Li. Renormalized entropy solutions for degenerate parabolichyperbolic equations with timespace dependent coefficients. Communications on Pure & Applied Analysis, 2013, 12 (3) : 11631182. doi: 10.3934/cpaa.2013.12.1163 
[10] 
Franco Obersnel, Pierpaolo Omari. Multiple bounded variation solutions of a capillarity problem. Conference Publications, 2011, 2011 (Special) : 11291137. doi: 10.3934/proc.2011.2011.1129 
[11] 
Roberto Alicandro, Andrea Braides, Marco Cicalese. $L^\infty$ jenergies on discontinuous functions. Discrete & Continuous Dynamical Systems  A, 2005, 12 (5) : 905928. doi: 10.3934/dcds.2005.12.905 
[12] 
CaiPing Liu. Some characterizations and applications on strongly $\alpha$preinvex and strongly $\alpha$invex functions. Journal of Industrial & Management Optimization, 2008, 4 (4) : 727738. doi: 10.3934/jimo.2008.4.727 
[13] 
Julien Jimenez. Scalar conservation law with discontinuous flux in a bounded domain. Conference Publications, 2007, 2007 (Special) : 520530. doi: 10.3934/proc.2007.2007.520 
[14] 
Jian Liu, Sihem Mesnager, Lusheng Chen. Variation on correlation immune Boolean and vectorial functions. Advances in Mathematics of Communications, 2016, 10 (4) : 895919. doi: 10.3934/amc.2016048 
[15] 
Renato C. Calleja, Alessandra Celletti, Rafael de la Llave. Construction of response functions in forced strongly dissipative systems. Discrete & Continuous Dynamical Systems  A, 2013, 33 (10) : 44114433. doi: 10.3934/dcds.2013.33.4411 
[16] 
Ciprian Preda, Petre Preda, Adriana Petre. On the asymptotic behavior of an exponentially bounded, strongly continuous cocycle over a semiflow. Communications on Pure & Applied Analysis, 2009, 8 (5) : 16371645. doi: 10.3934/cpaa.2009.8.1637 
[17] 
Karim Boulabiar, Gerard Buskes and Gleb Sirotkin. A strongly diagonal power of algebraic order bounded disjointness preserving operators. Electronic Research Announcements, 2003, 9: 9498. 
[18] 
G. P. Trachanas, Nikolaos B. Zographopoulos. A strongly singular parabolic problem on an unbounded domain. Communications on Pure & Applied Analysis, 2014, 13 (2) : 789809. doi: 10.3934/cpaa.2014.13.789 
[19] 
Maria Alessandra Ragusa. Parabolic systems with non continuous coefficients. Conference Publications, 2003, 2003 (Special) : 727733. doi: 10.3934/proc.2003.2003.727 
[20] 
Sofia Giuffrè, Giovanna Idone. On linear and nonlinear elliptic boundary value problems in the plane with discontinuous coefficients. Discrete & Continuous Dynamical Systems  A, 2011, 31 (4) : 13471363. doi: 10.3934/dcds.2011.31.1347 
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