Related papers: Erratum: Degenerate diffusion with a drift potenti…
In this contribution we prove the existence of weak solutions to degenerate parabolic systems arising from the coupled moisture movement, transport of dissolved species and heat transfer through partially saturated porous materials.…
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…
Several problems, issued from physics, biology or the medical science, lead to parabolic equations set in two sub-domains separated by a membrane with selective permeability to specific molecules. The corresponding boundary conditions,…
The large time behaviour of nonnegative solutions to a quasilinear degenerate diffusion equation with a source term depending solely on the gradient is investigated. After a suitable rescaling of time, convergence to a unique profile is…
In this paper, we consider the small viscosity limit problem for the isentropic compressible Navier-Stokes equations in a 2D exterior domain with impermeable boundary conditions , and the corresponding Euler equations have vortex sheet…
We establish a linear $L^p$ rate of convergence, $1<p<\infty$, with respect to the viscosity $\varepsilon$ for the vanishing viscosity process of semiconcave solutions of Hamilton-Jacobi equations by regularizing the PDE with the…
The advection-diffusion equation can be approximated by a one-dimensional diffusion equation in Lagrangian coordinates along the directions of compression of fluid elements (the stable manifold). This result holds in any number of…
We study a fractional diffusion problem in the divergence form in one space dimension. We define a notion of the viscosity solution. We prove existence of viscosity solutions to the fractional diffusion problem with the Dirichlet boundary…
We deal with the obstacle problem for the porous medium equation in the slow diffusion regime $m>1$. Our main interest is to treat fairly irregular obstacles assuming only boundedness and lower semicontinuity. In particular, the considered…
In this paper, we consider a singular limit problem for a diffuse interface model for two immiscible compressible viscous fluids. Via a relative entropy method, we obtain a convergence result for the low Mach number limit to a corresponding…
In this paper we study nonnegative, measure valued solutions of the initial value problem for one-dimensional drift-diffusion equations when the nonlinear diffusion is governed by an increasing $C^1$ function $\beta$ with $\lim_{r\to…
The influence of a small relative density difference on the displacement of two miscible liquids is studied experimentally in transparent 2D networks of micro channels. Both stable displacements in which the denser fluid enters at the…
In this paper, we investigate the convergence rate in the vanishing viscosity limit for solutions to superquadratic Hamilton--Jacobi equations with state constraints. For every $p>2$, we establish the rate of convergence for nonnegative…
This paper was originally published in June 2013 in JFM (vol. 725). There was one result concerning an expression of viscous dissipation in convective flows and a second result on the condition of applicability of the anelastic liquid…
Given two continuity equations with density-dependent velocities, we provide a new formula for the Wasserstein distance between the solutions in terms of the difference of velocities evaluated at the same density. The formula is…
This paper has been withdrawn by the author due to the incorrect application of the divergence theorem to Eqs 7, 8 and 9.
In this paper, some new upper bounds for Kullback-Leibler divergence(KL-divergence) based on $L^1, L^2$ and $L^\infty$ norms of density functions are discussed. Our findings unveil that the convergence in KL-divergence sense sandwiches…
A great challenge in the analysis of the discrepancy function D_N is to obtain universal lower bounds on the L-infty norm of D_N in dimensions d \geq 3. It follows from the average case bound of Klaus Roth that the L-infty norm of D_N is at…
We study a class of degenerate convection diffusion equations with a fractional nonlinear diffusion term. These equations are natural generalizations of anomalous diffusion equations, fractional conservations laws, local convection…
In this paper, the convergence of an algorithm for recovering the unknown kinematic viscosity of a two-dimensional incompressible, viscous fluid is studied. The algorithm of interest is a recursive feedback control-based algorithm that…