Existence of solutions to some nonlinear diffusion problems

Existence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.

Existence of Three Positive Solutions to Nonlinear Boundary Value Problems

Existence and Nonexistence of Global Positive Solutions to Nonlinear Diffusion Problems with Nonlinear Absorption through the Boundary

This paper deals with the existence and nonexistence of global positive solutions to ut = ∆ ln(1 + u) in Ω× (0,+∞), ∂ ln(1 + u) ∂n = √ 1 + u(ln(1 + u)) on ∂Ω× (0,+∞), and u(x, 0) = u0(x) in Ω. Here α ≥ 0 is a parameter, Ω ⊂ RN is a bounded smooth domain. After pointing out the mistakes in Global behavior of positive solutions to nonlinear diffusion problems with nonlinear absorption through the...

Characterizing the existence of large solutions for a class of sublinear problems with nonlinear diffusion

In this paper we characterize the existence of large solutions for a general class of sublinear elliptic problems of logistic type related to the porous media equation. Our main result shows that large solutions do exist if, and only if, the nonlinear diffusion is not too large. As a byproduct of the general theory developed by the authors in [2], those large solutions must be unstable with res...

Existence of Solutions for Some Noncoercive Elliptic Problems Involving Derivatives of Nonlinear Terms

We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a W 1,1 0 (Ω) solution which is distributional or entropic, according to the growth assumptions on a lower order term in divergence form. To Ildefonso: But of all these friends and lovers There is no one compares with you [9]