We obtain blow-up results for a wide class of nonlinear parabolic problems with nonlinearity of the Chipot-Weissler type in the gradient term. Some of these answer an open question concerning the nonexistence of positive solutions to the problem u t = Δu-λ∇u| 2p1/1+p1 + |u| P1-1 u in ℝR N ×]0,+∞[, u(x, 0) = u 0 (x) in ℝR N where λ > 0 is small, u 0 ∈ L loc (ℝR N ) with u 0 ≥ 0, when 1 < p 1 ≤ 1 + 2/N. For this purpose we use the method of "test function".
Blow-up results for parabolic inequalities with Chipot-Weissler nonlinearity in the gradient term / Piccirillo, A. M.; Toscano, Luisa; Toscano, S.. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - STAMPA. - 4:2(2004), pp. 209-234. [10.1515/ans-2004-0205]
Blow-up results for parabolic inequalities with Chipot-Weissler nonlinearity in the gradient term
A. M. PICCIRILLO;TOSCANO, LUISA;S. TOSCANO
2004
Abstract
We obtain blow-up results for a wide class of nonlinear parabolic problems with nonlinearity of the Chipot-Weissler type in the gradient term. Some of these answer an open question concerning the nonexistence of positive solutions to the problem u t = Δu-λ∇u| 2p1/1+p1 + |u| P1-1 u in ℝR N ×]0,+∞[, u(x, 0) = u 0 (x) in ℝR N where λ > 0 is small, u 0 ∈ L loc (ℝR N ) with u 0 ≥ 0, when 1 < p 1 ≤ 1 + 2/N. For this purpose we use the method of "test function".I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
