Linear parabolic equations with strong singular potentials

On Nonexistence of Baras–goldstein Type for Higher-order Parabolic Equations with Singular Potentials

The celebrated result by Baras and Goldstein (1984) established that the heat equation with singular inverse square potential in a smooth bounded domain Ω ⊂ RN , N ≥ 3, such that 0 ∈ Ω, ut = Δu+ c |x|2 u in Ω× (0, T ), u ∣∣ ∂Ω = 0, in the supercritical range c > cHardy(1) = ( N−2 2 )2 , does not have a solution for any nontrivial L1 initial data u0(x) ≥ 0 in Ω or for a positive measure. Namely,...

Title AN L^p-APPROACH TO SINGULAR LINEAR PARABOLIC EQUATIONS WITH LOWER ORDER TERMS

A Strong Regularity Result for Parabolic Equations

We consider a parabolic equation with a drift term u+b∇u−ut = 0. Under the condition divb = 0, we prove that solutions possess dramatically better regularity than those provided by standard theory. For example, we prove continuity of solutions when not even boundedness is expected.

Fluctuations of Parabolic Equations with Large Random Potentials

In this paper, we present a fluctuation analysis of a type of parabolic equations with large, highly oscillatory, random potentials around the homogenization limit. With a Feynman-Kac representation, the Kipnis-Varadhan’s method, and a quantitative martingale central limit theorem, we derive the asymptotic distribution of the rescaled error between heterogeneous and homogenized solutions under ...

On the singular fuzzy linear system of equations

The linear system of equations Ax = b where A = [aij ] in Cn.n is a crispsingular matrix and the right-hand side is a fuzzy vector is called a singularfuzzy linear system of equations. In this paper, solving singular fuzzy linearsystems of equations using generalized inverses such as Drazin inverse andpseudo-inverse are investigated.