Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

A Very Singular Solution of the Heat Equation with Absorption

Consider the Cauchy problem ut -du + u p ----0 on RN• (0, oo) (I.1) u > 0 on RN• (0, oo) (1.2) u(X, O) = c ~(x) on R, N, (1.3) where N _--> 1, c > 0 is a constant and ~(x) denotes the Dirac mass at the origin. A result of BREZlS and FRIEDMAN [6] asserts that if 1 < p < (N + 2)/N, then for every c > 0 there exists a unique 1 solution uc of (1.1)-(1.3). When p >= (N + 2)IN there is no solution of...

a quasilinear parabolic equation with inhomogeneous density and absorption

Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation.

The equation partial differential(t)u = u partial differential(xx)(2)u -(c-1)( partial differential(x)u)(2) is known in literature as a qualitative mathematical model of some biological phenomena. Here this equation is derived as a model of the groundwater flow in a water-absorbing fissurized porous rock; therefore, we refer to this equation as a filtration-absorption equation. A family of self...

Existence and uniqueness of very singular solutions for a fast diffusion equation with gradient absorption

Existence and uniqueness of radially symmetric self-similar very singular solutions are proved for the singular diffusion equation with gradient absorption ∂tu−∆pu+ |∇u| q = 0, in (0,∞)× R , where 2N/(N +1) < p < 2 and p/2 < q < p−N/(N +1), thereby extending previous results restricted to q > 1. AMS Subject Classification: 35K67, 35K92, 34B40, 34C11, 35B33.