Abstract
We study the degenerate differential equation
b(v)t - div a(v, del g(v)) = f on Q := (0, T) x Omega
with the initial condition b(v(0, .)) = b(v(0)) on Omega and boundary condition v = u on some part of the boundary Sigma := (0, T) x partial derivative Omega with g(u) equivalent to 0 a.e. on Sigma. The vector field a is assumed to satisfy the Leray-Lions conditions, and the functions b, g to be continuous, locally Lipschitz, nondecreasing and to satisfy the normalization condition b(0) = g(0) = 0 and the range condition R(b+g) = R. We assume also that g has a flat region [A(1), A(2)] with A(1) <= 0 <= A(2). Using Kruzhkov's method of doubling variables, we prove an existence and comparison result for renormalized entropy solutions.