Fujita type results for parabolic inequalities with gradient terms

被引：23

作者：

Filippucci, Roberta ^{[1
]}

Lombardi, Silvia ^{[2
]}

机构：

[1] Univ Perugia, Dipartimento Matemat & Informat, I-06123 Perugia, Italy

[2] Gran Sasso Sci Inst, Viale Francesco Crispi 7, I-67100 Laquila, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 268卷 / 05期

关键词：

Parabolic inequalities; Nonexistence of solutions; Global solutions; GLOBAL EXISTENCE; CAUCHY-PROBLEM; HEAT-EQUATION; NONUNIQUENESS; NONEXISTENCE; BLOWUP; DECAY;

D O I：

10.1016/j.jde.2019.09.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we give some Fujita type results for strongly p-coercive quasilinear parabolic differential inequalities with both a diffusion term and a dissipative term, whose prototype is given by u(t) - Delta(p)u >= a(x)u(q) - b(x)u(m) vertical bar del(u)vertical bar(s) in R-N x R+, u >= 0, u(x, 0) = u(0)(x)>= 0 in R-N, where p > 1, q > 0, 0 <= m < q, 0 < s <= p(q - m)/(q + 1) and a, b nonnegative weights which could be singular or degenerate. We prove the existence of Fujita type exponents qF , such that nonexistence of solutions for the inequality occurs when q < qF. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：1873 / 1910

页数：38

共 28 条

[1] Regularity and nonuniqueness results for parabolic problems arising in some physical models, having natural growth in the gradient [J].