Bestimmung und Anwendung von Vekua-Resolventen.
Blow-up for solutions of hyperbolic PDE and spacetime singularities
An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime singularities is naturally related to blow-up phenomena for nonlinear hyperbolic systems. These connections are explained and recent progress in applying the theory of hyperbolic equations in this field is presented. A direction which has turned out to be fruitful is that...
Boundary value problem for Fuchsian partial differential equations and reflection of singularities
Boundary value problems for generalized analytic functions of several complex variables
Boundary-Variation Solution of Eigenvalue Problems for Elliptic Operators.
Calcul de Weyl et opérateurs sous elliptiques
Calcul des singularités par la méthode des éléments finis
Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
Calcul symbolique et singularités des solutions des équations aux dérivées partielles non linéaires
Complex methods in non-linear analysis
Construction de solutions nulles et singulières pour des opérateurs de type principal
Construction de solutions singulières pour des équations aux dérivées partielles non linéaires
Construction de solutions singulières pour des équations aux dérivées partielles non linéaires
Continuation of analytic solutions of linear differential equations up to convex conical singularities
Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies
In this paper, a one-dimensional Euler-Lagrange equation associated with the total variation energy, and Euler-Lagrange equations generated by approximating total variations with linear growth, are considered. Each of the problems presented can be regarded as a governing equation for steady-states in solid-liquid phase transitions. On the basis of precise structural analysis for the solutions, the continuous dependence between the solution classes of approximating problems and that of the limiting...
Convergence of formal solutions of first order singular nonlinear partial differential equations in the complex domain
We study the convergence or divergence of formal (power series) solutions of first order nonlinear partial differential equations (SE) f(x,u,Dx u) = 0 with u(0)=0. Here the function f(x,u,ξ) is defined and holomorphic in a neighbourhood of a point and . The equation (SE) is said to be singular if f(0,0,ξ) ≡ 0 . The criterion of convergence of a formal solution of (SE) is given by a generalized form of the Poincaré condition which depends on each formal solution. In the case where the formal...
Convergence of formal solutions of first order singular partial differential equations of nilpotent type
Let (x,y,z) ∈ ℂ³. In this paper we shall study the solvability of singular first order partial differential equations of nilpotent type by the following typical example: , where . For this equation, our aim is to characterize the solvability on by using the Im P, Coker P and Ker P, and we give the exact forms of these sets.
Diffraction des singularités analytiques dans les problèmes aux limites de la physique mathématique par les méthodes de Kawai-Kashiwara et Sjöstrand
Distributions sphériques et équations différentielles singulières
Duality in the spaces of solutions of elliptic systems