Le problème de Cauchy ramifié linéaire pour des données à singularités algébriques
Le problème de Cauchy ramifié linéaire pour des données à singularités algébriques
Linearization and normal form of the Navier-Stokes equations with potential forces
Linearization of nonlinear differential equations. IV: Nonlinear second order partial differential equations equivalent to linear base equation.
Liouville theorem for Dunkl polyharmonic functions.
Local smooth solution and non-relativistic limit of radiation hydrodynamics equations.
Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains
We consider a class of semilinear elliptic problems in two- and three-dimensional domains with conical points. We introduce Sobolev spaces with detached asymptotics generated by the asymptotical behaviour of solutions of corresponding linearized problems near conical boundary points. We show that the corresponding nonlinear operator acting between these spaces is Frechet differentiable. Applying the local invertibility theorem we prove that the solution of the semilinear problem has the same asymptotic...
Long-time asymptotics of solutions to some nonlinear wave equations
In this paper, we survey some recent results on the asymptotic behavior, as time tends to infinity, of solutions to the Cauchy problems for the generalized Korteweg-de Vries-Burgers equation and the generalized Benjamin-Bona-Mahony-Burgers equation. The main results give higher-order terms of the asymptotic expansion of solutions.
Lp estimates of boundary integral equations for some nonlinear boundary value problems.
Maillet type theorem and Gevrey regularity in time of solutions to nonlinear partial differential equations
Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates
We are concerned with a 2D time harmonic wave propagation problem in a medium including a thin slot whose thickness ε is small with respect to the wavelength. In a previous article, we derived formally an asymptotic expansion of the solution with respect to ε using the method of matched asymptotic expansions. We also proved the existence and uniqueness of the terms of the asymptotics. In this paper, we complete the mathematical justification of our work by deriving optimal error estimates between...
Mémoire sur l'intégration des équations aux différences partielles de la Physique mathématique.
Mesures limites pour l’équation de Helmholtz dans le cas non captif
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 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
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...
Modified step variational iteration method for solving fractional biochemical reaction model.
Monge solutions for discontinuous hamiltonians
We consider an Hamilton-Jacobi equation of the formwhere is assumed Borel measurable and quasi-convex in . The notion of Monge solution, introduced by Newcomb and Su, is adapted to this setting making use of suitable metric devices. We establish the comparison principle for Monge sub and supersolution, existence and uniqueness for equation (1) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.
Monge solutions for discontinuous Hamiltonians
We consider an Hamilton-Jacobi equation of the form where H(x,p) is assumed Borel measurable and quasi-convex in p. The notion of Monge solution, introduced by Newcomb and Su, is adapted to this setting making use of suitable metric devices. We establish the comparison principle for Monge sub and supersolution, existence and uniqueness for equation ([see full text]) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also...
Monotone mappings and flows of viscous media.
Multibump solutions and asymptotic expansions for mesoscopic Allen-Cahn type equations
We consider a mesoscopic model for phase transitions in a periodic medium and we construct multibump solutions. The rational perturbative case is dealt with by explicit asymptotics.
Multibump solutions and asymptotic expansions for mesoscopic Allen-Cahn type equations
We consider a mesoscopic model for phase transitions in a periodic medium and we construct multibump solutions. The rational perturbative case is dealt with by explicit asymptotics.