Results 271 to 280 of about 255,795 (302)

Blow-Up and Extinction of Solutions

2015
For large nonlinearities, semilinear parabolic equations can undergo dramatic effects: blow-up or extinction. This means that solutions do not exist for all times or simply vanish in finite time, two scenarios that are the first signs of visible nonlinear effects. The mechanism is the same that for ordinary differential equations and the question is to
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Blowing-Up Behavior of Solutions

1992
The use of upper and lower solutions in D T for every T < ∞ leads to the existence of a global solution for the parabolic boundary-value problem. In case there is only a lower solution but no upper solution in D T for large T then it is possible that the solution grows unbounded in finite time. This chapter gives a detailed discussion of the blowing-up
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On the Blow-Up of Solutions of a Periodic Shallow Water Equation

Journal of Nonlinear Science, 2000
A blow-up result for the Cauchy problem for the periodic Camassa-Holm equation is given. Namely, it is proved that if the initial value \(u_0\in H^4(S)\), \(S=\mathbb{R}/\mathbb{Z}\), has at some point the slope less than \(-\sqrt{13/12}|u_0|_{H^1(S)}\), then the solution blows-up in finite time \(T\). The solution remains bounded in \([0;T)\), but its
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Existence and boundary blow-up rates of solutions for boundary blow-up elliptic systems

Nonlinear Analysis: Theory, Methods & Applications, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Mingxin, Wei, Lei
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Blow-up set of type I blowing up solutions for nonlinear parabolic systems

Mathematische Annalen, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fujishima, Yohei, Ishige, Kazuhiro, Maekawa, Hiroki   +2 more
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Extending solutions beyond blow-up

Nonlinear Analysis: Theory, Methods & Applications, 1996
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Blow-up of Solutions of a Class of Nonlinear Parabolic Equations

Journal of Partial Differential Equations, 1991
The authors discuss the effect of the terms \(u^ m\) and \(u^ p\) on the blow-up properties of the solutions of \[ u_ t-(u^ mu_ x)_ x = u^ p,\quad -R0,\quad \varphi(x)\geq 1,\quad \varphi(\pm R)=1, \] \[ -d/dx[\varphi^ md\varphi/dx ]_{x=\pm R}=1.
Zhang, Zhenbu, Jiang, Lishang
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Impulsive quenching and blow-up of solutions

Nonlinear Analysis: Theory, Methods & Applications, 1997
The author gives a review of the results obtained in the recent years on the quenching phenomena and blow-up of solutions of impulsive PDE. The paper consists of three sections dealing with impulsive parabolic quenching, impulsive hyperbolic quenching and impulsive parabolic blow-up, respectively.
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A new blow-up criterion of the strong solution to the quantum hydrodynamic model

Applied Mathematics Letters, 2021
Guangwu Wang
exaly  

The Blow-Up and Global Existence of Solution to Caputo–Hadamard Fractional Partial Differential Equation with Fractional Laplacian

Journal of Nonlinear Science, 2021
Changpin Li, Zhiqiang Li, Li Changpin
exaly