REGULARITY AND NONUNIQUENESS RESULTS FOR PARABOLIC PROBLEMS ARISING IN SOME PHYSICAL MODELS, HAVING NATURAL GROWTH IN THE GRADIENT

Abstract. In this paper we study the problem8><>: ut −∆u = β(u)|∇u|2 + f(x, t) in Q ≡ Ω × (0,+∞) u(x, t) = 0 on ∂Ω × (0,+∞), u(x, 0) = u0(x) in Ω, where Ω is a bounded regular domain, β is a positive nondecreasing function and f, u0 are positive functions satisfying some hypotheses of summability. Among others contribution the main one is to prove a wild non-uniqueness result