Remarks on the qualitative behavior of the undamped Klein-Gordon equation

Esquivel-Avila, Jorge A.

The search session has expired. Please query the service again.

Displaying similar documents to “Remarks on the qualitative behavior of the undamped Klein-Gordon equation”

Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping

Lorena Bociu, Irena Lasiecka (2008)

Applicationes Mathematicae

Similarity:

We focus on the blow-up in finite time of weak solutions to the wave equation with interior and boundary nonlinear sources and dissipations. Our central interest is the relationship of the sources and damping terms to the behavior of solutions. We prove that under specific conditions relating the sources and the dissipations (namely p > m and k > m), weak solutions blow up in finite time.

Remarks on the wave equation with a nonlinear term with respect to the velocity

Haraux, A. (1992)

Portugaliae mathematica

Similarity:

Blow-up of solutions for a viscoelastic equation with nonlinear damping

Yang Zhifeng (2008)

Open Mathematics

Similarity:

The initial boundary value problem for a viscoelastic equation with nonlinear damping in a bounded domain is considered. By modifying the method, which is put forward by Li, Tasi and Vitillaro, we sententiously proved that, under certain conditions, any solution blows up in finite time. The estimates of the life-span of solutions are also given. We generalize some earlier results concerning this equation.

Global existence for nonlinear system of wave equations in 3-D domains

Jianwei Yang (2011)

Applicationes Mathematicae

Similarity:

We study the initial-boundary problem for a nonlinear system of wave equations with Hamilton structure under Dirichlet's condition. We use the local-in-time Strichartz estimates from [Burq et al., J. Amer. Math. Soc. 21 (2008), 831-845], Morawetz-Pohožaev's identity derived in [Miao and Zhu, Nonlinear Anal. 67 (2007), 3136-3151], and an a priori estimate of the solutions restricted to the boundary to show the existence of global and unique solutions.

Blowup of solutions of a nonlinear wave equation.

Benaissa, Abbes, Messaoudi, Salim A. (2002)

Journal of Applied Mathematics

Similarity:

Initial value problems in elasticity

Rolf Leis (1992)

Banach Center Publications

Similarity:

Blow-Up of Solutions of Nonlinear Wave Equations in Three Space Dimensions.

Fritz John (1979)

Manuscripta mathematica

Similarity:

Weak solutions to the initial boundary value problem for a semilinear wave equation with damping and source terms

Petronela Radu (2008)

Applicationes Mathematicae

Similarity:

We show local existence of solutions to the initial boundary value problem corresponding to a semilinear wave equation with interior damping and source terms. The difficulty in dealing with these two competitive forces comes from the fact that the source term is not a locally Lipschitz function from H¹(Ω) into L²(Ω) as typically assumed in the literature. The strategy behind the proof is based on the physics of the problem, so it does not use the damping present in the equation. The...

Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension

Frank Merle, Hatem Zaag (2009-2010)

Séminaire Équations aux dérivées partielles

Similarity:

We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution $u (x, t)$ , the graph $x \mapsto T (x)$ of its blow-up points and $𝒮 \subset ℝ$ the set of all characteristic points and show that $𝒮$ is locally finite. Finally, given $x_{0} \in 𝒮$ , we show that in selfsimilar variables, the solution decomposes into a decoupled sum of (at least two) solitons, with alternate signs and that...

Blow-up for nonlinear wave equations with slowly decaying data.

Hiroyuki Takamura (1994)

Mathematische Zeitschrift

Similarity:

Evolution equations in non-cylindrical domains

Piermarco Cannarsa, Giuseppe Da Prato, Jean-Paul Zolésio (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

We develolp a new method to solve an evolution equation in a non-cylindrical domain, by reduction to an abstract evolution equation..

Counterexamples to local existence for nonlinear wave equations

Hans Lindblad (1994)

Journées équations aux dérivées partielles

Similarity:

The wave map problem. Small data critical regularity

Igor Rodnianski (2005-2006)

Séminaire Bourbaki

Similarity:

The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is $(2 + 1)$ , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory....