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Mesures limites pour l’équation de Helmholtz dans le cas non captif

Jean-François Bony (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

Cet article est consacré à l’étude des mesures limites associées à la solution de l’équation de Helmholtz avec un terme source se concentrant en un point. Le potentiel est supposé C ∞ et l’opérateur non-captif. La solution de l’équation de Schrödinger semi-classique s’écrit alors micro-localement comme somme finie de distributions lagrangiennes. Sous une hypothèse géométrique, qui généralise l’hypothèse du viriel, on en déduit que la mesure limite existe et qu’elle vérifie des propriétés standard....

Modeling of vibration for functionally graded beams

Gülsemay Yiğit, Ali Şahin, Mustafa Bayram (2016)

Open Mathematics

In this study, a vibration problem of Euler-Bernoulli beam manufactured with Functionally Graded Material (FGM), which is modelled by fourth-order partial differential equations with variable coefficients, is examined by using the Adomian Decomposition Method (ADM).The method is one of the useful and powerful methods which can be easily applied to linear and nonlinear initial and boundary value problems. As to functionally graded materials, they are composites mixed by two or more materials at a...

On Borel summable solutions of the multidimensional heat equation

Sławomir Michalik (2012)

Annales Polonici Mathematici

We give a new characterisation of Borel summability of formal power series solutions to the n-dimensional heat equation in terms of holomorphic properties of the integral means of the Cauchy data. We also derive the Borel sum for the summable formal solutions.

On representations of real analytic functions by monogenic functions

Hongfen Yuan (2019)

Czechoslovak Mathematical Journal

Using the method of normalized systems of functions, we study one representation of real analytic functions by monogenic functions (i.e., solutions of Dirac equations), which is an Almansi’s formula of infinite order. As applications of the representation, we construct solutions of the inhomogeneous Dirac and poly-Dirac equations in Clifford analysis.

On the eigenfunction expansion method for semilinear dissipative equations in bounded domains and the Kuramoto-Sivashinsky equation in a ball

V. V. Varlamov (2001)

Studia Mathematica

Presented herein is a method of constructing solutions of semilinear dissipative evolution equations in bounded domains. For small initial data this approach permits one to represent the solution in the form of an eigenfunction expansion series and to calculate the higher-order long-time asymptotics. It is applied to the spatially 3D Kuramoto-Sivashinsky equation in the unit ball B in the linearly stable case. A global-in-time mild solution is constructed in the space C ⁰ ( [ 0 , ∞ ) , H ₀ s ( B ) ) , s < 2, and the uniqueness...

Opérateurs de Fuchs non linéaires

Patrice Pongérard, Claude Wagschal (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

On se propose d’étudier des équations aux dérivées partielles non linéaires du type de Fuchs au sens de Baouendi-Goulaouic ([1] et [2]) dans des espaces de fonctions suffisamment différentiables par rapport à la variable fuchsienne et dans des espaces de Gevrey par rapport aux autres variables. Les méthodes utilisées reposent sur le formalisme des séries formelles Gevrey développé dans [13] et adapté aux équations du type de Fuchs dans [6] et [7]. On obtient ainsi des théorèmes qui généralisent...

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