Related papers: Linear Parabolic Problems in Random Moving Domains
In this paper, we present an extensive study of linearly forced isotropic turbulence. By using an analytical method, we identified two parametric choices that are new to our knowledge. We proved that the underlying nonlinear dynamical…
A cyclic random motion at finite velocity with orthogonal directions is considered in the plane and in $\mathbb{R}^3$. We obtain in both cases the explicit conditional distributions of the position of the moving particle when the number of…
We study the strong solvability of the nonstationary Stokes problem with non-zero divergence in a bounded domain.
We study linear nonautonomous parabolic systems with dynamic boundary conditions. Next, we apply these results to show a theorem of local existence and uniqueness of a classical solution to a second order quasilinear system with nonlinear…
We study a doubly nonlinear parabolic problem arising in the modeling of gas transport in pipelines. Using convexity arguments and relative entropy estimates we show uniform bounds and exponential stability of discrete approximations…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
We present a model for the dynamics of fluid vesicles in linear flow which consistently includes thermal fluctuations and nonlinear coupling between different modes. At the transition between tank-treading and tumbling, we predict a…
We consider a parabolic version of the mass transport problem, and show that it converges to a solution of the original mass transport problem under suitable conditions on the cost function, and initial and target domains.
We study coupled non-linear parabolic equations for a fluid described by a material density and a temperature, both functions of space and time. In one dimension, we find some stationary solutions corresponding to fixing the temperature on…
In cylindrical domain, we consider the nonstationary flow with prescribed inflow and outflow, modelled with Navier-Stokes equations under the slip boundary conditions. Using smallness of some derivatives of inflow function, external force…
Unconventional cycles provide a useful didactic resource to discuss the second law of thermodynamics applied to thermal motors and their efficiency. In most cases they involve a negative slope, linear process that presents an adiabatic…
By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three classes of transformations corresponding to…
This is the second part of a two parts work on the analysis of heat-type equations on manifolds with fibered boundary equipped with a $\Phi$-metric. This setting generalizes the asymptotically conical (scattering) spaces and includes…
We investigate the behavior of dynamic shape design problems for fluid flow at large time horizon. In particular, we shall compare the shape solutions of a dynamic shape optimization problem with that of a stationary problem and show that…
We study well-posedness of degenerate mixed-type parabolic-hyperbolic equations $$ \partial_tu+\text{div}\big(f(u)\big)=\mathcal{L}[b(u)] $$ on bounded domains with general Dirichlet boundary/exterior conditions. The nonlocal diffusion…
The past decades have seen increasing interest in modelling uncertainty by heterogeneous methods, combining probability and interval analysis, especially for assessing parameter uncertainty in engineering models. A unifying mathematical…
This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order and whose derivative satisfies some growth condition at infinity. This class contains most of the classical families of transcendental…
Here we study the Dirichlet problem for first order linear and quasi-linear hyperbolic PDEs on a simply connected bounded domain of $\R^2$, where the domain has an interior outflow set and a mere inflow boundary. By means of a Lyapunov…
In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the…
The aim article is to contribute to the definition of a versatile language for metastability in the context of partial differential equations of evolutive type. A general framework suited for parabolic equations in one dimensional bounded…