On the theory of entropy suband supersolutions of nonlinear degenerate parabolic equations

We consider a second-order nonlinear degenerate anisotropic parabolic equation in the case when flux vector is only continuous and nonnegative diffusion matrix bounded measurable. The concepts of entropy sub- supersolution Cauchy problem are introduced, so that solution this problem, understood sense Chen-Perthame, both an supersolution. It established maximum subsolutions also subsolution problem. This result used to prove existence largest (and smallest supersolution). shown solutions.