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We consider a class of Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions that describe possible short-range interactions between the binary mixture and the solid boundary. In the presence of surface diffusion on…
In many cases, analytic solutions of partial differential equations may not be possible. For practical problems, it is more reasonable to carry out computational solutions. However, the standard grid in the finite difference approximation…
We consider the initial-boundary value problem for the incompressible two-dimensional micropolar fluid model with angular viscosity in the upper half-plane. This model describes the motion of viscous fluids with microstructure. The global…
We introduce a variational structure for the Fourier-Cattaneo (FC) system which is a second-order hyperbolic system. This variational structure is inspired by the large-deviation rate functional for the Kac process which is closely linked…
We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann…
In this thesis we introduce the concept of a guided dynamical system, and exploit this idea to solve various problems in functional equations and PDE's. Our main results are 1) a necessary and sufficient condition for unique-solvability of…
We consider a discrete dynamical system on a pseudo-Riemannian manifold and we determine the concept of a hyperbolic set for it. We insert a condition in the definition of a hyperbolic set which implies to the unique decomposition of a part…
We study a one-dimensional nonlinear hyperbolic-parabolic initial boundary value problem occurring in the theory of thermoelasticity. We prove existence and uniqueness of the local-in-time strong solution. Also, some global-in-time weak…
We consider a two-phase elliptic-parabolic moving boundary problem modelling an evaporation front in a porous medium. Our main result is a proof of short-time existence and uniqueness of strong solutions to the corresponding nonlinear…
The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…
We investigate systems of degenerate parabolic equations idealizing reactive solute transport in porous media. Taking advantage of the inherent structure of the system that allows to deduce a scalar Generalized Porous Medium Equation for…
We provide a systematic approach for deducing statistical limit laws via martingale-coboundary decomposition, for nonuniformly hyperbolic systems with slowly contracting and expanding directions. In particular, if the associated return time…
Consider the planar restricted $(N+1)$-body problem with trajectories of the $N(\ge 2)$ primaries forming a collision-free periodic solution of the $N$-body problem, for any positive energy $h$ and directions $\theta_{\pm} \in [0, 2\pi)$,…
We develop a complete description of the class of conformal relativistic dissipative fluids of divergence form, following the formalism carried out by Geroch, Lindblom and Pennisi. This type of theories is fully described in terms of…
The aim of the paper is to study local Hadamard well-posedness for wave equation with an hyperbolic dynamical boundary condition, internal and/or boundary damping and sources for initial data in the natural energy space. Moreover the…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
We address the system of partial differential equations modeling motion of an elastic body interacting with an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by a…
We prove for the $N$-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level $h>0$ of the motion can also be chosen arbitrarily. Our approach is…
This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the…
We use the hyperbolic subdiffusion equation with fractional time derivatives (the generalized Cattaneo equation) to study the transport process of electrolytes in media where subdiffusion occurs. In this model the flux is delayed in a…