Existence and uniqueness of radial solutions for fresh/salt water interface equation in a confined aquifer

A priori gradient bounds for fully nonlinear parabolic equations and applications to porous medium models

“…Step 2: Checking Assumption 1.1 iii) Inequality (1.9) of Assumption 1.1 iii) can be written as Assume (3.7) and let B(0, R) be a ball of radius R > 0. Then we have, by [9] for d > 1 and by [5] for d = 1, existence and uniqueness of weak radial solutions of Problem (1.7), (1.2) with Neumann boundary conditions. Moreover the solutions satisfy uniform bounds similar to (1.13) and (1.11), but on the ball B(0, R).…”

“…Then we have, by [9] for d > 1 and by [5] for d = 1, existence and uniqueness of weak radial solutions of Problem (1.7), (1.2) with Neumann boundary conditions. Moreover the solutions satisfy uniform bounds similar to (1.13) and (1.11), but on the ball B(0, R).…”

“…Therefore Corollary 3.4 appears to be a kind of extension of this result to the non radial case, and for smooth solutions. Finally let us mention an existence and uniqueness result in [9] for radial nondecreasing solutions with u(x, t) ∈ […”