Conservation laws for equations related to soil water equations.
Conservation laws for the nonlinear Schrödinger equation
Construction de solutions ramifiées autour de deux hypersurfaces caractéristiques simples pour des opérateurs quasi-linéaires
Construction de solutions singulières pour des équations aux dérivées partielles non linéaires
Construction solutions of PDE in parametric form.
Continuation of analytic solutions of linear differential equations up to convex conical singularities
Continuous selections of solution sets to second order evolution equations.
Continuous spectrum of a fourth order nonhomogeneous elliptic equation with variable exponent.
Convergence and Order Reduction of Runge-Kutta Schemes Applied to Evolutionary Problems in Partial Differential Equations.
Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics
We prove the convergence at a large scale of a non-local first order equation to an anisotropic mean curvature motion. The equation is an eikonal-type equation with a velocity depending in a non-local way on the solution itself, which arises in the theory of dislocation dynamics. We show that if an anisotropic mean curvature motion is approximated by equations of this type then it is always of variational type, whereas the converse is true only in dimension two.
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.
Convergence Rates of the POD–Greedy Method
Iterative approximation algorithms are successfully applied in parametric approximation tasks. In particular, reduced basis methods make use of the so-called Greedy algorithm for approximating solution sets of parametrized partial differential equations. Recently, a priori convergence rate statements for this algorithm have been given (Buffa et al. 2009, Binev et al. 2010). The goal of the current study is the extension to time-dependent problems, which are typically approximated using the POD–Greedy...
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.
Correction to "Uniqueness for the harmonic map flow from surfaces to general targets".
Counterexamples to Hölmgren's uniqueness for analytic non linear Cauchy problem.
Das Iterationsverfahren für eine partielle Differentialgleichung vierter Ordnung
Deformation from symmetry for Schrödinger equations of higher order on unbounded domains.
Deforming convex hypersurfaces by the square root of the scalar curvature.
Die Lösung der partiellen Differentialgleichung mit gewissen Nebenbedingungen