Characterization of Jacobian varieties in terms of soliton equations.
Classical Solutions of the Chain Equation. I.
Colombeau's theory and shock wave solutions for systems of PDEs.
Complex methods in non-linear analysis
Conservation laws for the nonlinear Schrödinger equation
Construction de solutions singulières pour des équations aux dérivées partielles non linéaires
Construction solutions of PDE in parametric form.
Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem
We study convergence of formal power series along families of formal or analytic vector fields. One of our results says that if a formal power series converges along a family of vector fields, then it also converges along their commutators. Using this theorem and a result of T. Morimoto, we prove analyticity of formal solutions for a class of nonlinear singular PDEs. In the proofs we use results from control theory.
Convex integration of non-linear systems of partial differential equations
Geometrical techniques are employed to prove a global existence theorem for -solutions to underdetermined systems of non-linear order partial differential equations, , which satisfy certain convexity conditions. The solutions are not unique, but satisfy given approximations on lower order derivatives. The main result, which includes the relative case generalizes the work of M. Gromov on non-linear first order systems.
Convolution equations in the space of Laplace distributions
A formal solution of a nonlinear equation P(D)u = g(u) in 2 variables is constructed using the Laplace transformation and a convolution equation. We assume some conditions on the characteristic set Char P.
Differential equations, Spencer cohomology, and computing resolutions.
Differential inequalities for a nonlinear partial differential equation of the fourth order
Eindutigkeitsaussagen für das Tricomi-Problem im ... für eine Klasse nichtlinearer Gleichungen gemischten Typs.
Évolution d'une onde simple pour des équations non-linéaires générales
Existence locale de solutions pour l’équation de Monge-Ampère réelle
Existence of C... local Solutions for the Monge-Ampère equation.
Existence results for a fourth order partial differential equation arising in condensed matter physics
We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation which nonlinearity is the determinant of the Hessian matrix of the solution. We consider this model in a bounded domain of the real plane and study its stationary solutions both when the geometry of this domain is arbitrary and when it is the unit ball and the solution is radially symmetric. We also consider the initial-boundary value problem...
Existence theorems for a partial differential equation of the fourth order
Finite dimensional behavior for weakly damped driven Schrödinger equations
Formal and Convergent Solutions of Singular Partial Differential Equations.