Critical criteria of Fujita type for a system of inhomogeneous wave inequalities in exterior domains

Jleli, Mohamed; Samet, Bessem; Ye, Dong

doi:10.1016/j.jde.2019.09.051

Cited by 30 publications

(7 citation statements)

References 19 publications

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“…In the above, Ω ⊂ R N is either the exterior of a ball or an unbounded cone-like domain; for other results on hyperbolic inequalities in exterior domains see [14,15,18]. We observe that solutions of (8) are also required to satisfy (7).…”

Section: Introduction and The Main Resultsmentioning

confidence: 96%

Higher order evolution inequalities with nonlinear convolution terms

Filippucci¹,

Ghergu²

2022

Preprint

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We are concerned with the study of existence and nonexistence of weak solutions towhere N, k, m ≥ 1 are positive integers, p, q > 0 and u i ∈ L 1 loc (R N ) for 0 ≤ i ≤ k − 1. We assume that K is a radial positive and continuous function which decreases in a neighbourhood of infinity. In the above problem, K * |u| p denotes the standard convolution operation between K(|x|) and |u| p . We obtain necessary conditions on N, m, k, p and q such that the above problem has solutions. Our analysis emphasizes the role played by the sign of ∂ k−1 u ∂t k−1 .

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Section: Introduction and The Main Resultsmentioning

confidence: 96%

Higher order evolution inequalities with nonlinear convolution terms

Filippucci¹,

Ghergu²

2022

Preprint

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“…Remark 1.3. Recently, there are lots of papers studied the critical exponent of non-global solutions to inequalities, see for example [12,13,20,21,25,26,[31][32][33]. Theorem 1.1 is also true for the Cauchy problem of the following inhomogeneous pseudo-parabolic inequality with a space-time forcing term:…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…Remark Recently, there are lots of papers studied the critical exponent of non‐global solutions to inequalities, see for example [12, 13, 20, 21, 25, 26, 31–33]. Theorem 1.1 is also true for the Cauchy problem of the following inhomogeneous pseudo‐parabolic inequality with a space‐time forcing term:

$$ \left\{\begin{array}{llll}&amp; {u}_t-k\Delta {u}_t\ge \Delta u&#x0002B;{\left&#x0007C;u\right&#x0007C;}&#x0005E;p&#x0002B;{t}&#x0005E;{\sigma}\omega (x)\kern0.30em &amp; &amp; \mathrm{for}\kern0.30em x\in {\mathrm{\mathbb{R}}}&#x0005E;n,t&gt;0,\\ {}&amp; u\left(x,0\right)&#x0003D;{u}_0(x)&amp; &amp; \mathrm{for}\kern0.30em x\in {\mathrm{\mathbb{R}}}&#x0005E;n.\end{array}\right.

…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Critical exponent of non‐global solutions for an inhomogeneous pseudo‐parabolic equation with space‐time forcing term

Zhao,

Zhou

2023

Math Methods in App Sciences

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We investigate the critical exponent of non‐global solutions to the following inhomogeneous pseudo‐parabolic equation with a space‐time forcing term: where is an integer; , , and are three constants; and . By obtaining a priori estimate for the solutions and the contradiction argument, we show that there exists a critical exponent: such that the problem does not admit any global solutions when and . Our obtained results show that the forcing term induces an interesting phenomenon of continuity/discontinuity of the critical exponent depending on the dimension . Namely, we found that when , ; when ; and when , . Furthermore, with when and when coincides with the critical exponent of the above problem with .

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“…For more references related to the study of evolution equations and inequalities in exterior domains, see for example [20, 21, 23, 32, 36].…”

Section: Introductionmentioning

confidence: 99%

Higher-order evolution inequalities involving convection and Hardy-Leray potential terms in a bounded domain

Chen¹,

Jleli²,

Samet³

2023

Proceedings of the Edinburgh Mathematical Society

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We consider a class of nonlinear higher-order evolution inequalities posed in $(0,\infty)\times B_1\backslash\{0\}$ , subject to inhomogeneous Dirichlet-type boundary conditions, where B1 is the unit ball in $\mathbb{R}^N$ . The considered class involves differential operators of the form \begin{equation*} \mathcal{L}_{\mu_1,\mu_2}=-\Delta +\frac{\mu_1}{|x|^2}x\cdot \nabla +\frac{\mu_2}{|x|^2},\qquad x\in \mathbb{R}^N\backslash\{0\}, \end{equation*} where $\mu_1\in \mathbb{R}$ and $\mu_2\geq -\left(\frac{\mu_1-N+2}{2}\right)^2$ . Optimal criteria for the nonexistence of weak solutions are established. Our study yields naturally optimal nonexistence results for the corresponding class of elliptic inequalities. Notice that no restriction on the sign of solutions is imposed.

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Critical criteria of Fujita type for a system of inhomogeneous wave inequalities in exterior domains

Cited by 30 publications

References 19 publications

Higher order evolution inequalities with nonlinear convolution terms

Higher order evolution inequalities with nonlinear convolution terms

Critical exponent of non‐global solutions for an inhomogeneous pseudo‐parabolic equation with space‐time forcing term

Higher-order evolution inequalities involving convection and Hardy-Leray potential terms in a bounded domain

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