Results 261 to 270 of about 11,046,071 (291)

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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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 bounded solutions of differential equations

2003
The paper is a generalization of a ``negative'' result telling that on infinite-dimensional Banach spaces bounded solutions of differential equations blowing up in finite time could exist. Unlike the known counter-examples, here, the autonomous case is considered and the construction is valid on all infinite-dimensional Banach spaces.
Komornik, Vilmos, Martinez, Patrick, Pierre, Michel, Vancostenoble, Judith   +3 more
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A rescaling algorithm for the numerical calculation of blowing‐up solutions

Communications on Pure and Applied Mathematics, 1988
A method is developed for computing solutions of certain nonlinear evolution equations near a developing singularity in space-time. The main tools are rescaling and mesh refinement; in essence, the method uses a varying spatial grid and time step, linked at each point of space-time to the magnitude of the computed solution.
Berger, Marsha, Kohn, Robert V.
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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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Application of Solution Blow Spinning for Rapid Fabrication of Gelatin/Nylon 66 Nanofibrous Film

Foods, 2021
Di Wu, Meng Xu, Di Wu
exaly  

A new blow-up criterion of the strong solution to the quantum hydrodynamic model

Applied Mathematics Letters, 2021
Guangwu Wang
exaly