Conservation laws for equations related to soil water equations.
Construction de solutions ramifiées autour de deux hypersurfaces caractéristiques simples pour des opérateurs quasi-linéaires
Continuous selections of solution sets to second order evolution 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.
Counterexamples to Hölmgren's uniqueness for analytic non linear Cauchy problem.