Galerkin approximations to non-linear pseudo-parabolic partial differential equations. (Short Communication).
Galerkin approximations to non-linear pseudo-parabolic partial differential equations.
Generalizations of Melin's inequality to systems
We discuss a recent necessary and sufficient condition for Melin's inequality for a class of systems of pseudodifferential operators.
Geometric proofs of composition theorems for generalized Fourier integral operators.
Geometry of stationary sets for the wave equation in . The case of finitely supported initial data: An announcement.
Gevrey hypoellipticity for partial differential equations with characteristics of higher multiplicity.
Global time estimates for solutions to equations of dissipative type
Global time estimates of norms of solutions to general strictly hyperbolic partial differential equations are considered. The case of special interest in this paper are equations exhibiting the dissipative behaviour. Results are applied to discuss time decay estimates for Fokker-Planck equations and for wave type equations with negative mass.
Gradient flows of the entropy for jump processes
We introduce a new transport distance between probability measures on that is built from a Lévy jump kernel. It is defined via a non-local variant of the Benamou–Brenier formula. We study geometric and topological properties of this distance, in particular we prove existence of geodesics. For translation invariant jump kernels we identify the semigroup generated by the associated non-local operator as the gradient flow of the relative entropy w.r.t. the new distance and show that the entropy is...