Related papers: Long time behavior for a dissipative shallow water…
This article discusses the analyticity and the long-time asymptotic behavior of solutions to space-time fractional diffusion equations in $\mathbb{R}^d$. By a Laplace transform argument, we prove that the decay rate of the solution as…
We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…
Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…
We introduce a simple model of the time evolution of a binary mixture of compressible fluids including the thermal effects. Despite its apparent simplicity, the model is thermodynamically consistent admitting an entropy balance equation. We…
In this paper, we analyse the long-time behavior of solutions to a coupled system describing the motion of a rigid disk in a 2D viscous incompressible fluid. Following previous approaches, we look at the problem in the system of coordinates…
A long-time behavior of solutions to a nonlinear plate model subject to non-conservative and non-dissipative effects and nonlinear damping is considered. The model under study is a prototype for a suspension bridge under the effects of…
These lectures present the analysis of stability and control of long time behavior of PDE models described by nonlinear evolutions of hyperbolic type. Specific examples of the models under consideration include: (i) nonlinear systems of…
We consider a model for internal waves described by a zero order pseudo-differential Hamiltonian $P$ damped by a second order viscosity term $i \nu Q$. Under Morse-Smale or similar weaker global conditions on the classical dynamics, we…
We study the dynamic behaviour of solutions to a fourth-order quasilinear degenerate parabolic equation for large times arising in fluid dynamical applications. The degeneracy occurs both with respect to the unknown and with respect to the…
In this paper we consider a tank containing fluid and we want to estimate the horizontal currents when the fluid surface height is measured. The fluid motion is described by shallow water equations in two horizontal dimensions. We build a…
We consider $\mathbf L^\infty$ solutions to $2\times 2$ systems of conservation laws. For genuinely nonlinear systems we prove that finite entropy solutions (in particular entropy solutions, if a uniformly convex entropy exists) belong to…
We consider the Benjamin-Ono equation on the torus with an additional damping term on the smallest Fourier modes (cos and sin). We first prove global well-posedness of this equation in $L^2_{r,0}(\mathbb{T})$. Then, we describe the weak…
In this paper, we consider a problem inspired by the real-world need to identify the topographical features of ocean basins. Specifically we consider the problem of estimating the bottom impermeable boundary to an inviscid, incompressible,…
We establish $L^2$-exponential decay properties for linear dissipative kinetic equations, including the time-relaxation and Fokker-Planck models, in bounded spatial domains with general boundary conditions that may not conserve mass. Their…
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
We propose a model for a two dimensional, associative water-like lattice gas with one single variable representing both long and short-range interactions. The corresponding hamiltonian was solved exactly, by state enumeration in a finite…
In this paper we develop two models for the steady states and evolution of two dimensional isothermal self gravitating and rotating incompressible gas which are based on the hydrodynamic equations for stratified fluid. The first model is…
We review here the derivation of many of the most important models that appear in the literature (mainly in coastal oceanography) for the description of waves in shallow water. We show that these models can be obtained using various…
This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…
This work concerns the analysis of electromagnetic dispersive media modelled by generalized Lorentz models. More precisely, this paper is the second of two articles dedicated to the long time behaviour of solutions of Maxwell's equations in…