Related papers: Stability of a Hot Smoluchowski Fluid
We study a strongly coupled system consisting of a parabolic equation and a singular Hamilton-Jacobi equation in one space dimension. This system describes the dynamics of dislocation densities in a material submitted to an exterior applied…
Our objective is to prove existence of a solution to the Dirichlet problem for an equation arising in the theory of radiation hydrodynamics to deal with the radiating energy in transparent media. We study its stationary equation with…
We consider the flow of a generalized non-Newtonian incompressible heat-conducting fluid in a~bounded two-dimensional domain, subject to Dirichlet boundary conditions for velocity and temperature. The fluid obeys a power-law constitutive…
This paper investigates the large-time behavior of a buoyancy-driven fluid without thermal diffusion under Navier-slip boundary conditions in a bounded domain with Lipschitz-continuous second derivatives. After establishing improved…
We study the relationship between the Regularity and Dirichlet boundary value problems for parabolic equations of the form $Lu=\text{div}(A \nabla u)-u_t=0$ in Lip$(1,1/2)$ time-varying cylinders, where the coefficient matrix $A = \left[…
We consider the mixed Dirichlet-conormal problem for the heat equation on cylindrical domains with a bounded and Lipschitz base $\Omega\subset \mathbb{R}^d$ and a time-dependent separation $\Lambda$. Under certain mild regularity…
In this paper we obtain the continuity of attractors for nonlinear parabolic equations with nonlinear boundary conditions when the boundary of the domain varies very rapidly as a parameter $\epsilon$ goes to zero. We consider the case where…
We examine various density results related to the solutions of the non-local heat equation at a specific time slice, focusing on two distinct models: one with homogeneous Dirichlet boundary condition and the other with singular boundary…
Locally bounded, local weak solutions to a doubly nonlinear parabolic equation, which models the multi-phase transition of a material, is shown to be locally continuous. Moreover, an explicit modulus of continuity is given. The effect of…
We prove that a large class of parabolic final value problems is well posed.This results via explicit Hilbert spaces that characterise the data yielding existence, uniqueness and stability of solutions. This data space is the graph normed…
Convergence to stationary solutions in fully nonlinear parabolic systems with general nonlinear boundary conditions is shown in situations where the set of stationary solutions creates a $C^2$-manifold of finite dimension which is normally…
Solving numerically hydrodynamical problems of incompressible fluids raises the question of handling first order derivatives (those of pressure) in a closed container and determining its boundary conditions. We research several pressure…
We review some models of granular materials fluidized by means of external forces such as: random homogeneous forcing with damping, vibrating plates, flow in an inclined channel and flow in a double well potential. All these systems show…
We consider a differential model describing nonisothermal fast phase separation processes taking place in a three-dimensional bounded domain. This model consists of a viscous Cahn-Hilliard equation characterized by the presence of an…
Transport of cold atoms in shallow optical lattices is characterized by slow, nonstationary momentum relaxation. We here develop a projector operator method able to derive in this case a generalized Smoluchowski equation for the position…
In this paper, the one-dimensional compressible Navier-Stokes system with outer pressure boundary conditions is investigated. Under some suitable assumptions, we prove that the specific volume and the temperature are bounded from below and…
An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be written as a Laplacian growth model regularized by a `kinetic undercooling' boundary condition. We study the linear stability of uniformly…
We provide very mild sufficient conditions for space-time domains (non-necessarily cylindrical) which ensure that the continuous Dirichlet problem and the H\"older Dirichlet problem are well-posed, for any parabolic operator in divergence…
A fluid occupying a mechanically isolated vessel with walls kept at spatially non-uniform temperature is in the long run expected to reach the spatially inhomogeneous steady state. Irrespective of the initial conditions the velocity field…
We study a basic linear elliptic equation on a lower dimensional rectifiable set $S$ in $\mathbb{R}^N$ with the Neumann boundary data. Set $S$ is a support of a finite Borel measure $\mu$. We will use the measure theoretic tools to…