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Spreading and vanishing in nonlinear diffusion problems with free boundaries

Yihong Du, Bendong Lou (2015)

Journal of the European Mathematical Society

We study nonlinear diffusion problems of the form u t = u x x + f ( u ) with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For special f ( u ) of the Fisher-KPP type, the problem was investigated by Du and Lin [DL]. Here we consider much more general nonlinear terms. For any f ( u ) which is C 1 and satisfies f ( 0 ) = 0 , we show that the omega limit set ω ( u ) of every bounded positive solution is determined by a stationary solution....

Stabilité des solitons de l’équation de Landau-Lifshitz à anisotropie planaire

André de Laire, Philippe Gravejat (2014/2015)

Séminaire Laurent Schwartz — EDP et applications

Cet exposé présente plusieurs résultats récents quant à la stabilité des solitons sombres de l’équation de Landau-Lifshitz à anisotropie planaire, en particulier, quant à la stabilité orbitale des trains (bien préparés) de solitons gris [16] et à la stabilité asymptotique de ces mêmes solitons [2].

Stability estimates for an inverse problem for the linear Boltzmann equation.

Rolci Cipolatti, Carlos M. Motta, Nilson C. Roberty (2006)

Revista Matemática Complutense

In this paper we consider the inverse problem of recovering the total extinction coefficient and the collision kernel for the time-dependent Boltzmann equation via boundary measurements. We obtain stability estimates for the extinction coefficient in terms of the albedo operator and also an identification result for the collision kernel.

Stability for approximation methods of the one-dimensional Kobayashi-Warren-Carter system

Hiroshi Watanabe, Ken Shirakawa (2014)

Mathematica Bohemica

A one-dimensional version of a gradient system, known as “Kobayashi-Warren-Carter system”, is considered. In view of the difficulty of the uniqueness, we here set our goal to ensure a “stability” which comes out in the approximation approaches to the solutions. Based on this, the Main Theorem concludes that there is an admissible range of approximation differences, and in the scope of this range, any approximation method leads to a uniform type of solutions having a certain common features. Further,...

Stability of the inverse problem in potential scattering at fixed energy

Plamen Stefanov (1990)

Annales de l'institut Fourier

We prove an estimate of the kind ∥ q 1 - q 2 ∥ L ∞ ≤ C ϕ ( ∥ A q 1 - A q 2 ∥ R , 3 / 2 - 1 / 2 ) , where A q i ( ω , θ ) , i = 1 , 2 is the scattering amplitude related to the compactly supported potential q i ( x ) at a fixed energy level k = const., ϕ ( t ) = ( - ln t ) - δ , 0 < δ < 1 and ∥ · ∥ R , 3 / 2 - 1 / 2 is a suitably defined norm.

Currently displaying 1441 – 1460 of 1901