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.
The initial value problem for the equations of magnetohydrodynamic type in non-cylindrical domains.
By using the spectral Galerkin method, we prove the existence of weak solutions for a system of equations of magnetohydrodynamic type in non-cylindrical domains.
The Isolated Point Singularity Problem for the Coupled Yang-Mills Equations in Higher Dimensions.
The jump problem for mixed-type equations with defects on the type change line.
The Laplace method of the linear partial differential equations of the -th order
The Lie-algebraic discrete approximation scheme for evolution equations with Dirichlet/Neumann data.
The lifespan of spherically symmetric solutions of the compressible Euler equations outside an impermeable sphere
The logarithmic gradient of the kernel of the heat equation with drift on a Riemannian manifold.
The multidimensional -transform and its use in solution of partial difference equations
The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes
We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region .
The positive radial solutions of a class of semilinear elliptic equations.
The problem of regular isometric embeddings and the Monge-Ampère equation of hyperbolic type