The Role of Critical Exponents in Blow-Up Theorems: The Sequel

By Keng Deng, H. Levine. 2000

589 citations recorded by the source corpus.

Subfields: Applied Mathematics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/a5f4c3851ce22cab9e4be38fdb728014b481d947

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In Applied Mathematics

In Public Health, Environmental and Occupational Health

Citations in the corpus

Blow-up for p-Laplacian parabolic equations (2003, background): “When Ω = R , the Fujita exponents have been calculated; see [7, 8, 9, 10] and also the survey papers [3, 12].”
Small data blow-up of $L^2$-solution for the nonlinear Schrödinger equation without gauge invariance (2011, background): “For the nonlinear heat equation and the damped wave equation with the same type nonlinearity as |u| p , it is well known that the exponent p = 1 + 2/n, which is often referred to as the “Fujita exponent”, is the threshold between the small data global existence and blow-up of solutions (see [9, 3, 1”
Towards a Unified Approach to Nonexistence of Solutions for a Class of Differential Inequalities (2004, unknown): “See also [7], [8], [28],[32] and [35].”
Finite time blow up for critical wave equations in high dimensions (2004, methodology): “We only give a brief summary here and refer the reader to [St], [L], [ DL ] and a recent paper [JZ] for details.”
Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption (2006, background): “See also the survey papers by Levine [21], Deng and Levine [2], and the pioneering paper [5] by H.”
Recent results and open problems on parabolic equations with gradient nonlinearities. (2001, background): “We refer for these to the books and survey articles [6, 41, 33, 57, 54, 14].”
Critical extinction and blow‐up exponents for fast diffusive p‐Laplacian with sources (2007, unknown): “From then on, it has been shown that critical Fujita exponent expresses important features for different evolutionary equations, and has been extended to some other directions, we refer to [2] for a survey of the literature for these problems.”
Cauchy problems of semilinear pseudo-parabolic equations ✩ (2009, result): “We refer to the survey papers [6,19], the recent works [1,20,21,25,32–36] and the references therein for a detailed account.”
Nonexistence of weak solutions for some degenerate elliptic and parabolic problems on $ {\Bbb R}^n $ (2001, methodology): “In this case, our method shows that for these kind of problems the critical Fujita exponents always belong to the “blow-up” case (see [MP1], [MP2], [MP3]), without using any argument based on the knowledge of the fundamental solution of the evolution operator or comparison principles [L], [ DL ], [G”