Displaying similar documents to “Blow up of mechanical systems with a homogeneous energy.”

Blow-up of a nonlocal p-Laplacian evolution equation with critical initial energy

Yang Liu, Pengju Lv, Chaojiu Da (2016)

Annales Polonici Mathematici

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This paper is concerned with the initial boundary value problem for a nonlocal p-Laplacian evolution equation with critical initial energy. In the framework of the energy method, we construct an unstable set and establish its invariance. Finally, the finite time blow-up of solutions is derived by a combination of the unstable set and the concavity method.

Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain

Valeria Banica (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than ( T - t ) - 1 , the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain. ...

Instability of equilibria in dimension three

Marco Brunella (1998)

Annales de l'institut Fourier

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In this paper we show that if v is an analytic vector field on ℝ 3 having an isolated singular point at 0, then there exists a trajectory of v which converges to 0 in the past or in the future. The proof is based on certain results concerning desingularizaton of vector fields in dimension three and on index-type arguments .

Blow up and near soliton dynamics for the L 2 critical gKdV equation

Yvan Martel, Frank Merle, Pierre Raphaël (2011-2012)

Séminaire Laurent Schwartz — EDP et applications

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These notes present the main results of [, , ] concerning the mass critical (gKdV) equation u t + ( u x x + u 5 ) x = 0 for initial data in H 1 close to the soliton. These works revisit the blow up phenomenon close to the family of solitons in several directions: definition of the stable blow up and classification of all possible behaviors in a suitable functional setting, description of the minimal mass blow up in H 1 , construction of various exotic blow up rates in H 1 , including grow up in infinite time. ...