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 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 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 Rothe method and time periodic solutions to the Navier-Stokes equations and equations of magnetohydrodynamics
The existence of a periodic solution of a nonlinear equation is proved. The theory developed may be used to prove the existence of a periodic solution of the variational formulation of the Navier-Stokes equations or the equations of magnetohydrodynamics. The proof of the main existence theorem is based on Rothe method in combination with the Galerkin method, using the Brouwer fixed point theorem.
The Tzitzeica surface as solution of PDE systems.
The use of Cerami sequences in critical point theory.
Three solutions of a quasilinear elliptic problem near resonance
T-Periodic Solutions of Time Dependent Hamiltonian Systems with a Potential Vanishing at Infinity.
Traveling wave solutions of the heat flow of director fields
Two-scale convergence of a model for flow in a partially fissured medium.
Tzitzeica theory -- opportunity for reflection in mathematics.