[. W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z, vol.18385, issue.3, pp.311-341, 1983.

S. [. Caffarelli and . Salsa, A geometric approach to free boundary problems, Graduate Studies in Mathematics, vol.68, 2005.
DOI : 10.1090/gsm/068

J. [. Caffarelli and . Vazquez, Viscosity solutions for the porous medium equation, Differential equations: La Pietra, pp.13-26, 1996.

J. Carrillo, Entropy Solutions for Nonlinear Degenerate Problems, Archive for Rational Mechanics and Analysis, vol.147, issue.4, pp.269-361, 1999.
DOI : 10.1007/s002050050152

I. C. Kim, B. Perthame, P. E. And, . Souganidis-[-dg-]-e, R. Dibenedetto et al., Local behavior of solutions of an elliptic-parabolic equation, Archive for Rational Mechanics and, Analysis, vol.97, issue.1, pp.1-17, 1987.

A. Friedman, A hierarchy of cancer models and their mathematical challenges, Discrete Contin, Dyn. Syst. Ser. B, vol.4, issue.1, pp.147-159, 2002.

I. C. Kim, Uniqueness and Existence Results on the Hele-Shaw and the Stefan Problems, Archive for Rational Mechanics and Analysis, vol.168, issue.4, pp.299-328, 2003.
DOI : 10.1007/s00205-003-0251-z

. C. Kp-]-i, N. Kim, and . Po?ár, Nonlinear elliptic-parabolic problems, Arch. Ration. Mech. Anal, vol.210, issue.3, pp.975-1020, 2013.

. S. Lfj-+-]-j, H. B. Lowengrub, F. Frieboes, Y. Jin, . Chuang et al., Nonlinear modelling of cancer: bridging the gap between cells and tumours, Nonlinearity, vol.2323, issue.11, pp.1-91, 2010.

M. [. Perthame, N. Tang, and . Vauchelet, Traveling wave solution of the Hele???Shaw model of tumor growth with nutrient, Mathematical Models and Methods in Applied Sciences, vol.24, issue.13
DOI : 10.1142/S0218202514500316

URL : https://hal.archives-ouvertes.fr/hal-00931399

F. [. Perthame, M. Quirós, N. Tang, and . Vauchelet, Derivation of a Hele-Shaw type system from a cell model with active motion, Interfaces and Free Boundaries, pp.489-508, 2015.

B. Perthame, F. Quirós, and J. L. Vázquez, The Hele???Shaw Asymptotics for Mechanical Models of Tumor Growth, Archive for Rational Mechanics and Analysis, vol.34, issue.2, pp.93-127, 2014.
DOI : 10.1007/s00205-013-0704-y

URL : https://hal.archives-ouvertes.fr/hal-00831932

J. L. Vázquez, The porous medium equation, 2007.
DOI : 10.1093/acprof:oso/9780198569039.001.0001

. Department-of-mathematics, L. Ucla, and . Angeles, CA 90095, USA E-mail address, I.C. Kim: ikim@math.ucla