The dynamics of a tied body against an obstacle
The Ekeland's variational principle for vector-valued multifunctions.
The existence and uniqueness theorem in Biot's consolidation theory
Existence and uniqueness theorem is established for a variational problem including Biot's model of consolidation of clay. The proof of existence is constructive and uses the compactness method. Error estimates for the approximate solution obtained by a method combining finite elements and Euler's backward method are given.
The existence of Ginzburg-Landau solutions on the plane by a direct variational method
The extended tanh-mehtod for finding traveling wave solutions of nonlinear evolution equations.
The FBI transform, operators with nonsmooth coefficients and the nonlinear wave equation
The aim of this work is threefold. First we set up a calculus for partial differential operators with nonsmooth coefficients which is based on the FBI (Fourier-Bros-Iagolnitzer) transform. Then, using this calculus, we prove a weaker version of the Strichartz estimates for second order hyperbolic equations with nonsmooth coefficients. Finally, we apply these new Strichartz estimates to second order nonlinear hyperbolic equations and improve the local theory, i.e. prove local well-posedness for initial...
The fictitious domain method for the mixed finite element approximation of the wave equation
The Fourier method for the linear partial differential equations of the -th order
The Fourier spectral method for the Sivashinsky equation.
The Fourier transform on and its application to Cauchy problems for linear partial differential equations
The Fuchsian Cauchy problem.
The fundamental solution for a consistent complex model of the shallow shell equations.
The fundamental solution of a modified Oseen problem.
The general form of local bilinear functions
The scalar product of the FEM basis functions with non-intersecting supports vanishes. This property is generalized and the concept of local bilinear functional in a Hilbert space is introduced. The general form of such functionals in the spaces and is given.
The generalized Cauchy problem with data on two surfaces for a quasilinear analytic system.
The geometric optics for a class of hyperbolic second order operators with Hölder continuous coefficients with respect to time
The geometry of the space of Cauchy data of nonlinear PDEs
First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given in many equivalent ways - for instance, by means of Grassmann bundles. In this paper we generalize it by means of flag bundles, and develop the corresponding theory for higher-oder and infinite-order jet bundles. We show that this is a natural geometric framework...
The group structure of supergravity
The version of Eulerian-Lagrangian mixed discontinuous finite element methods for advection-diffusion problems.
The heat equation on manifolds as a gradient flow in the Wasserstein space
We study the gradient flow for the relative entropy functional on probability measures over a riemannian manifold. To this aim we present a notion of a riemannian structure on the Wasserstein space. If the Ricci curvature is bounded below we establish existence and contractivity of the gradient flow using a discrete approximation scheme. Furthermore we show that its trajectories coincide with solutions to the heat equation.