Related papers: A singular controllability problem with vanishing …
The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space $\mathbb{R}^{3}_{+}$ is rigorously proved under a Navier-slip boundary condition for velocity and…
The purpose of this paper is to study the vanishing viscosity limit for the d-dimensional Navier--Stokes equations in the whole space: \begin{equation*} \begin{cases} \partial_tu^\varepsilon+u^\varepsilon\cdot \nabla…
We analyze the sidewise controllability for the variable coefficients one-dimensional wave equation. The control is acting on one extreme of the string with the aim that the solution tracks a given path at the other free end. This sidewise…
In a three-dimensional bounded domain $\Omega$ we consider the compressible Navier-Stokes equations for a barotropic fluid with general non-linear density dependent viscosities and no-slip boundary conditions. A nonlinear drag term is added…
This paper is devoted to the controllability analysis of a class of linear control systems in a Hilbert space. It is proposed to use the minimum energy controls of a reduced lumped parameter system for solving the infinite dimensional…
We prove the uniqueness for viscosity solutions of a differential equation involving the infinity-Laplacian with a variable exponent. A version of the Harnack's inequality is derived for this minimax problem.
We consider the Cauchy problem for a stochastic scalar parabolic-hyperbolic equation in any space dimension with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional…
The paper is devoted to studying the 1D viscous Burgers equation controlled by an external force. It is assumed that the initial state is essentially bounded, with no decay condition at infinity, and the control is a trigonometric…
We consider the null controllability problem for the wave equation, and analyse a stabilized finite element method formulated on a global, unstructured spacetime mesh. We prove error estimates for the approximate control given by the…
In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary…
We consider the problem of the numerical approximation of the linear controllability of waves. All our experiments are done in a bounded domain \Omega of the plane, with Dirichlet boundary conditions and internal control. We use a Galerkin…
We study the wave equation in an interval with two linearly moving endpoints. We give the exact solution by a series formula, then we show that the energy of the solution decay at the rate $1/t$. We also establish observability results, at…
In this work, we investigate the small-time global exact controllability of the Navier-Stokes equation, both towards the null equilibrium state and towards weak trajectories. We consider a viscous incompressible fluid evolving within a…
A general class of linear advective PDEs, whose leading order term is of viscous dissipative type, is considered. It is proved that beyond the limit of the essential spectrum of the underlying inviscid operator, the eigenvalues of the…
We consider generalized gradient systems with rate-independent and rate-dependent dissipation potentials. We provide a general framework for performing a vanishing-viscosity limit leading to the notion of parametrized and true…
In this article, we consider a stochastic linear quadratic control problem with partial observation. A near optimal control in the weak formulation is characterized. The main features of this paper are the presence of the control in the…
A slender-jet model for the pinching of a liquid column is considered in the limit of vanishing viscosity. We find the model to develop a singularity in the gradients of the local radius and the velocity at a finite thread radius, so it…
In this paper, we study the asymptotic stability of rarefaction waves for the compressible isentropic Navier-Stokes equations with density-dependent viscosity. First, a weak solution around a rarefaction wave to the Cauchy problem is…
Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\big\|u(t,\cdot)-u^\ve(t,\cdot)\big\|_{\L^1}= \O(1)(1+t)\cdot \sqrt\ve|\ln\ve|$ on the distance between an exact BV solution $u$ and…
In this paper we study linear parabolic equations on a finite oriented starshaped network; the equations are coupled by transmission conditions set at the inner node, which do not impose continuity on the unknown. We consider this problem…