Scattering, scattering inverse et équations d'évolutions non linéaires
Scattering, transformations spectrales et équations d'évolution non linéaire II
Semi-discrétisation en temps pour les équations d'évolution paraboliques lorsque l'opérateur dépend du temps
Semielliptic singularities
Semigroup formulation of Rothe's method: application to parabolic problems
A semilinear parabolic equation in a Banach space is considered. The purpose of this paper is to show the dependence of an error estimate for Rothe's method on the regularity of initial data. The proofs are done using a semigroup theory and Taylor spectral representation.
Simplifying numerical solution of constrained PDE systems through involutive completion
When analysing general systems of PDEs, it is important first to find the involutive form of the initial system. This is because the properties of the system cannot in general be determined if the system is not involutive. We show that the notion of involutivity is also interesting from the numerical point of view. The use of the involutive form of the system allows one to consider quite general situations in a unified way. We illustrate our approach on the numerical solution of several flow equations...
Simplifying numerical solution of constrained PDE systems through involutive completion
When analysing general systems of PDEs, it is important first to find the involutive form of the initial system. This is because the properties of the system cannot in general be determined if the system is not involutive. We show that the notion of involutivity is also interesting from the numerical point of view. The use of the involutive form of the system allows one to consider quite general situations in a unified way. We illustrate our approach on the numerical solution of several flow equations...
Singularités éliminables pour des équations semi-linéaires
Étant donné un opérateur différentiel d’ordre sur un ouvert de , un compact de , et , nous montrons que toute solution de “ sur ” est solution de “ sur ” dès que la -capacité de est nulle. Cette condition s’avère nécessaire quand est un opérateur elliptique d’ordre 2. Dans ce cas, nous montrons aussi que où est une mesure de Radon bornée sur , a une solution si et seulement si ne charge pas les ensembles de -capacité nulle.
Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data
The purpose of this paper is to derive the error estimates for discretization in time of a semilinear parabolic equation in a Banach space. The estimates are given in the norm of the space for when the initial condition is not regular.
Solution de l'équation d'Euler en dimension 2
Solution of singular and nonsingular initial and boundary value problems by modified variational iteration method.
Solutions analytiques de l'équation d'Euler d'un fluide compressible
Solutions hyperfonctions du problème de Cauchy
Solutions indéfiniment différentiables d’un système d’équations aux différences et application aux systèmes d’équations aux dérivées partielles
Dans cette note, nous prouvons l’existence de solutions indéfiniment différentiables d’un système de deux équations aux différences et appliquons la technique utilisée à l’étude des systèmes d’équations linéaires aux dérivées partielles.Dans chaque cas, on montre que les solutions sont les premières composantes des solutions d’un système matriciel que nous étudions.
Solvability for a nonlinear coupled system of Kirchhoff type for the beam equations with nonlocal boundary conditions.
Solvability for semilinear PDE with multiple characteristics
We prove local solvability in Gevrey spaces for a class of semilinear partial differential equations. The linear part admits characteristics of multiplicity k ≥ 2 and data are fixed in , 1 < σ < k/(k-1). The nonlinearity, containing derivatives of lower order, is assumed of class with respect to all variables.
Solvability of boundary value problems for operator-differential equations of mixed type: the degenerate case.
Solvable nonlinear evolution PDEs in multidimensional space.
Solving the Degenerate Complex Monge-Ampère Equation with One Concentrated Singularity.
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations