Viscosity solutions for quasilinear degenerate parabolic equations of porous medium type Cristina BrandleJuan Vazquez 35K6535K15viscosity solutionsdegenerate parabolic equationswell-posedness We consider the Cauchy Problem for the class of nonlinear parabolic equations of the form $$u_t=a(u)\Delta u+|\nabla u|^2,$$ with a function $a(u)$ that vanishes at $u=0$. Because of the degenerate character of the coefficient $a$ the usual concept of viscosity solution in the sense of Crandall-Evans-Lions has to be modified to include the behaviour at the free boundary. We prove that the problem is well-posed in a suitable class of viscosity solutions. Agreement with the concept of weak solution is also shown. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2565 10.1512/iumj.2005.54.2565 en Indiana Univ. Math. J. 54 (2005) 817 - 860 state-of-the-art mathematics http://iumj.org/access/