Singular Behavior in Nonlinear Parabolic Equations

Large time behavior for some nonlinear degenerate parabolic equations

We study the asymptotic behavior of Lipschitz continuous solutions of nonlinear degenerate parabolic equations in the periodic setting. Our results apply to a large class of Hamilton-Jacobi-Bellman equations. Defining Σ as the set where the diffusion vanishes, i.e., where the equation is totally degenerate, we obtain the convergence when the equation is uniformly parabolic outside Σ and, on Σ, ...

Front propagation in nonlinear parabolic equations

We study existence and stability of travelling waves for nonlinear convection diffusion equations in the 1-D Euclidean space. The diffusion coefficient depends on the gradient in analogy with the p-Laplacian and may be degenerate. Unconditional stability is established with respect to initial data perturbations in L(R). Running head: Poincaré inequality and P.-S. condition

Attractors for Parabolic Equations with Nonlinear Boundary Conditions, Critical Exponents, and Singular Initial Data

Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain

We establish comparison and existence theorems of viscosity solutions of the initial-boundary value problem for some singular degenerate parabolic partial di/erential equations with nonlinear oblique derivative boundary conditions. The theorems cover the capillary problem for the mean curvature 1ow equation and apply to more general Neumann-type boundary problems for parabolic equations in the ...

Singular Nonlinear Elliptic Equations in R

This paper deals with existence, uniqueness and regularity of positive generalized solutions of singular nonlinear equations of the form −∆u + a(x)u = h(x)u−γ in R where a, h are given, not necessarily continuous functions, and γ is a positive number. We explore both situations where a, h are radial functions, with a being eventually identically zero, and cases where no symmetry is required fro...