ABSTRACT
In the case ip = k = 0, the evolution equation obtained from (1.1-2) is well known (several examples can be found, e.g., in [8, 13, 14]) and, according to the choice of 7, it is connected with the Stefan problem, the porous media equation, or the Hele-Shaw model. To be precise, the last case corresponds to the position 7 = 7/, where H denotes the Heaviside graph (H(r) = 0 if r < 0, 7/(0) = [0,1], H(r) = 1 if r > 0), the Stefan problem comes out for 7(7*) = r + H(r), r G IR, while the porous media equation is associated with 7(r) = I r^V, r G IR, for some 77 G (0,1). Our assumption on 7 plainly covers these cases, since we only ask for the existence of a constant Co such that
(1.5)
(1.6)
i.e., a superquadratic growth at infinity. In this framework, we are basically interested in discussing existence of solutions for
(1.7)
Our aim is thus extending or generalizing some previous analysis performed on (1.1-4) either with null kernels (much work on that has been done, see [14] and the references proposed in [13]) or in particular settings for 7 (see [2, 4, 5] and references therein).
