Related papers: The evolving surface Cahn-Hilliard equation with a…
We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
In this paper, we present a new computational framework to approximate a Cahn-Hilliard-Navier-Stokes model with variable density and degenerate mobility that preserves the mass of the mixture, the pointwise bounds of the density and the…
In first order formulation of pure gravity, we find a new class of solutions to the equations of motion represented by degenerate four-geometries. These configurations are described by non- invertible tetrads with two zero eigenvalues and…
We investigate the homogeneous Dirichlet problem in uniformly convex domains for a large class of degenerate elliptic equations with singular zero order term. In particular we establish sharp existence and uniqueness results of positive…
We propose a new Cahn-Hilliard phase field model coupled to incompressible viscoelasticity at large strains, obtained from a diffuse interface mixture model and formulated in the Eulerian configuration. A new kind of diffusive…
This article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth-order degenerate parabolic equations of gradient flow type. The underlying metric is a Wasserstein-like…
We consider weak solutions to very singular parabolic equations involving a one-Laplace-type operator, which is singular and degenerate, and a $p$-Laplace-type operator with $\frac{2n}{n+2}<p<\infty$, where $n\ge 2$ denotes the space…
We use the method of sliding paraboloids to establish a Harnack inequality for linear, degenerate and singular elliptic equation with unbounded lower order terms. The equations we consider include uniformly elliptic equations and linearized…
We consider a non-isothermal modified Cahn--Hilliard equation which was previously analyzed by M. Grasselli et al. Such an equation is characterized by an inertial term and a viscous term and it is coupled with a hyperbolic heat equation.…
We study existence and uniqueness of solutions to a class of nonlinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To…
We extend the doubly degenerate Cahn-Hilliard (DDCH) models for isotropic surface diffusion, which yield more accurate approximations than classical degenerate Cahn-Hilliard (DCH) models, to the anisotropic case. We consider both weak and…
We consider the Cahn--Hilliard/Navier--Stokes system with non-degenerate mobility in the space-periodic case, describing the flow of two viscous immiscible and incompressible Newtonian fluids with matched densities. We identify sufficient…
We investigate the long-time behavior of a nonlocal Cahn-Hilliard equation in a bounded domain $\Omega\subset\mathbb{R}^d$ $(d\in\{2,3\})$, subject to a kinetic rate-dependent nonlocal dynamic boundary condition. The kinetic rate $1/L$,…
We consider a relaxation of the viscous Cahn-Hilliard equation induced by the second-order inertial term~$u_{tt}$. The equation also contains a semilinear term $f(u)$ of "singular" type. Namely, the function $f$ is defined only on a bounded…
The paper presents a model of lateral phase separation in a two component material surface. The resulting fourth order nonlinear PDE can be seen as a Cahn-Hilliard equation posed on a time-dependent surface. Only elementary tangential…
We consider a class of Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions that describe possible short-range interactions between the binary mixture and the solid boundary. In the presence of surface diffusion on…
Studying the (long-term) behavior of the K\"ahler-Ricci flow on mildly singular varieties, one is naturally lead to study weak solutions of degenerate parabolic complex Monge-Amp\'ere equations. The purpose of this article, the first of a…
We introduce a new method which resolves the problem of regularity and compactness of entropy solutions for nonlinear degenerate parabolic equations under non-degeneracy conditions on the sphere. In particular, we address a problem of…
We consider formal matched asymptotics to show the convergence of a degenerate area preserving surface Allen-Cahn equation to its sharp interface limit of area preserving geodesic curvature flow. The degeneracy results from a surface de…
We analyze the weak solution concept for the Fornberg-Whitham equation in case of traveling waves with a piecewise smooth profile function. The existence of discontinuous weak traveling wave solutions is shown by means of analysis of a…