Perturbations numériques des évolutions parabolique et hyperbolique
Problèmes aux limites généraux pour des opérateurs différentiels paraboliques dans un domaine borné
De tels problèmes mixtes sont étudiés dans certains domaines non cylindriques, lorsque les conditions à l’instant initial sont celles de Cauchy, par l’intermédiaire de problèmes pseudo-différentiels sur le bord latéral du domaine. On donne des conditions qui permettent d’établir l’existence ou l’unicité de la solution.
Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions
Sufficient conditions for destabilizing effects of certain unilateral boundary conditions and for the existence of bifurcation points for spatial patterns to reaction-diffusion systems of the activator-inhibitor type are proved. The conditions are related with the mollification method employed to overcome difficulties connected with empty interiors of appropriate convex cones.
Regularity of solutions of parabolic equations with coefficients depending on t and parameters
The main object of this paper is to study the regularity with respect to the parameter h of solutions of the problem , . The continuity of u with respect to both h and t has been considered in [6].
Relaxation of optimal control problems in Lp-SPACES
We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an Lp-space (p < ∞). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.
Relaxation of optimal control problems in -spaces
We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an -space (). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.
Representation theorems and Fatou theorems for parabolic systems in the sense of Petrovskiĭ
Singularity analysis and integrability of a Burgers-type system of Foursov.
Speed-up of reaction-diffusion fronts by a line of fast diffusion
In these notes, we discuss a new model, proposed by H. Berestycki, J.-M. Roquejoffre and L. Rossi, to describe biological invasions in the plane when a strong diffusion takes place on a line. This model seems relevant to account for the effects of roads on the spreading of invasive species. In what follows, the diffusion on the line will either be modelled by the Laplacian operator, or the fractional Laplacian of order less than 1. Of interest to us is the asymptotic speed of spreading in the direction...
Stability for approximation methods of the one-dimensional Kobayashi-Warren-Carter system
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,...
Strong unique continuation for the Lamé system with Lipschitz coefficients in three dimensions
This paper studies the strong unique continuation property for the Lamé system of elasticity with variable Lamé coefficients λ, µin three dimensions, whereλ and μ are Lipschitz continuous and V∈L∞. The method is based on the Carleman estimate with polynomial weights for the Lamé operator.
Strong unique continuation for the Lamé system with Lipschitz coefficients in three dimensions*
This paper studies the strong unique continuation property for the Lamé system of elasticity with variable Lamé coefficients λ, µ in three dimensions, where λ and μ are Lipschitz continuous and V∈L∞. The method is based on the Carleman estimate with polynomial weights for the Lamé operator.
Sur la limitation des éleménts de la matrice fondamentale d'un systèeme parabolique
Sur l'intérabilité par rapport à l'accroissement du temps 0 ≤ θ < ∞ de la solution fondamentale spéciale de l'opérateur P parabolique
Sur l'unicité du problème de Cauchy dans une classe de fonctions non bornées
The dynamics of weakly interacting fronts in an adsorbate-induced phase transition model
Hildebrand et al. (1999) proposed an adsorbate-induced phase transition model. For this model, Takei et al. (2005) found several stationary and evolutionary patterns by numerical simulations. Due to bistability of the system, there appears a phase separation phenomenon and an interface separating these phases. In this paper, we introduce the equation describing the motion of two interfaces in and discuss an application. Moreover, we prove the existence of the traveling front solution which approximates...
The interior regularity and the Liouville property for the quasilinear parabolic systems
Uniqueness for the two-dimensional semiconductor equations in case of high carrier densities.
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Unstable periodic wave solutions of nerve axion diffusion equations.