Related papers: Weak solutions to the continuous coagulation model…
We consider a class of cross diffusion systems with degenerate (or porous media type) diffusion which is inspired by models in mathematical biology/ecology with zero self diffusions. Known techniques for scalar equations are no longer…
In this paper we consider the coalescence dynamics of a tagged particle moving in a random distribution of particles with volumes independently distributed according to a probability distribution (CTP model). We provide a rigorous…
We prove the existence of weak solutions to a viscoelastic phase separation problem in two space dimensions. The mathematical model consists of a Cahn-Hilliard-type equation for two-phase flows and the Peterlin-Navier-Stokes equations for…
The existence of global nonnegative weak solutions is proved for coupled one-dimensional lubrication systems that describe the evolution of nanoscopic bilayer thin polymer films that take account of Navier-slip or no-slip conditions at both…
A fluid-particle system of the inhomogeneous Navier-Stokes equations and Vlasov equation in the three dimensional space is considered in this paper. The coupling arises from the drag force in the fluid equations and the acceleration in the…
In this article we study the existence of solutions to a fourth-order nonlinear PDE related to crystal surface growth. The key difficulty in the equations comes from the mobility matrix, which depends on the gradient of the solution. When…
We propose a new approach to models of general compressible viscous fluids based on the concept of dissipative solutions. These are weak solutions satisfying the underlying equations modulo a defect measure. A dissipative solution coincides…
The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…
We introduce a new concepts of weak solution for the conservative stochastic Burgers equation in any dimension. The definition is based on weak solution concepts introduced by various authors in order to make sense of equations which do not…
We study a stochastic differential equation driven by a gamma process, for which we give results on the existence of weak solutions under conditions on the volatility function. To that end we provide results on the density process between…
We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a…
We prove the existence of weak solutions to kinetic flocking model with cut-off interaction function by using Schauder fixed pointed theorem and velocity averaging lemma. Under the natural assumption that the velocity support of the initial…
We investigate further the existence of solutions to kinetic models of chemotaxis. These are nonlinear transport-scattering equations with a quadratic nonlinearity which have been used to describe the motion of bacteria since the 80's when…
We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by the densities corresponding to an interacting particles…
Existence of global weak solutions to the continuous Oort-Hulst-Safronov (OHS) coagulation equation is investigated for coagulation kernels capturing a singularity near zero and growing linearly at infinity. The proof mainly relies on a…
In this paper, we study the global existence of solutions of the Cauchy problem for a class of weakly dissipative nonlinear dispersive wave equations…
We study the unsteady incompressible Navier-Stokes equations in three dimensions interacting with a non-linear flexible shell of Koiter type. This leads to a coupled system of non-linear PDEs where the moving part of the boundary is an…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a…
We prove the existence of a weak solution to a generalized quantum MHD equation in a 2-dimensional periodic box for large initial data. The existence of a global weak solution is established through a three-level approximation, energy…