Towards a Unified Approach to Nonexistence of Solutions for a Class of Differential Inequalities

2004 ◽  
Vol 72 (1) ◽  
pp. 129-162 ◽  
Author(s):  
Enzo Mitidieri ◽  
Stanislav I. Pohozaev
Keyword(s):  
Differential Inequalities ◽  
Unified Approach ◽  
Nonexistence Of Solutions

scholarly journals New Fujita type results for quasilinear parabolic differential inequalities with gradient dissipation terms

2021 ◽  
Vol 6 (10) ◽  
pp. 11482-11493
Author(s):  
Xiaomin Wang ◽  
◽  
Zhong Bo Fang
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Critical Exponents ◽  
Differential Inequality ◽  
Source Term ◽  
Differential Inequalities ◽  
Dissipation Term ◽  
Slow Decay ◽  
Nonexistence Of Solutions ◽  
Quasilinear Parabolic

<abstract><p>This paper deals with the new Fujita type results for Cauchy problem of a quasilinear parabolic differential inequality with both a source term and a gradient dissipation term. Specially, nonnegative weights may be singular or degenerate. Under the assumption of slow decay on initial data, we prove the existence of second critical exponents $ \mu^{*} $, such that the nonexistence of solutions for the inequality occurs when $ \mu &lt; \mu^{*} $.</p></abstract>

Blow-Up Results for Higher-Order Evolution Differential Inequalities in Exterior Domains

2019 ◽  
Vol 19 (2) ◽  
pp. 375-390
Author(s):  
Mohamed Jleli ◽  
Mokhtar Kirane ◽  
Bessem Samet
Keyword(s):  
Initial Data ◽  
Critical Exponents ◽  
Differential Inequality ◽  
Exterior Domain ◽  
Blow Up ◽  
Neumann Boundary ◽  
Higher Order ◽  
Differential Inequalities ◽  
Exterior Domains ◽  
Unified Approach

AbstractWe consider a higher-order evolution differential inequality in an exterior domain of {\mathbb{R}^{N}}, {N\geq 3}, with Dirichlet and Neumann boundary conditions. Using a unified approach, we obtain the critical exponents in the sense of Fujita for the considered problems. Moreover, the behavior of the solutions with respect to the initial data is discussed.

A Unified Approach to Study the Thermal Dynamics in Multilongitudinal Mode Semiconductor Lasers

2001 ◽  
Vol 20 (2) ◽  
pp. 159-169 ◽  
Author(s):  
M. Ganesh Madhan ◽  
P. R. Vaya ◽  
N. Gunasekaran
Keyword(s):  
Semiconductor Lasers ◽  
Unified Approach ◽  
Thermal Dynamics
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