Related papers: Fractional high order thin film equation: gradient…

We consider a Fokker-Planck equation which is coupled to an externally given time-dependent constraint on its first moment. This constraint introduces a Lagrange-multiplier which renders the equation nonlocal and nonlinear. In this paper we…

We consider a third order non-autonomous ODE that arises as a model of fluid accumulation in a two dimensional thin-film flow driven by surface tension and gravity. With the appropriate matching conditions, the equation describes the inner…

This paper studies the existence and asymptotic behavior of global weak solutions for a thin film equation with insoluble surfactant under the influence of gravitational, capillary and van der Waals forces. We prove the existence of global…

We prove that if $f:\mathbb{R}\to\mathbb{R}$ is Lipschitz continuous, then for every $H\in(0,1/4]$ there exists a probability space on which we can construct a fractional Brownian motion $X$ with Hurst parameter $H$, together with a process…

We prove the existence of nonnegative weak solutions to a class of second and fourth order nonautonomous nonlinear evolution equations with an explicitly time-dependent mobility function posed on the whole space $\mathbb{R}^d$, for…

We will give some regularity results about fractional diffusion-wave equations.

We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in $\mathbb{R}^2$. We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a…

The present paper is concerned with the analysis of two strongly coupled systems of degenerate parabolic partial differential equations arising in multiphase thin film flows. In particular, we consider the two-phase thin film Muskat problem…

We prove the existence of martingale solutions to stochastic thin-film equations in the physically relevant space dimension $d=2$. Conceptually, we rely on a stochastic Faedo-Galerkin approach using tensor-product linear finite elements in…

We find solutions that describe the levelling of a thin fluid film, comprising a non-Newtonian power-law fluid, that coats a substrate and evolves under the influence of surface tension. We consider the evolution from both periodic and…

We consider the stochastic thin-film equation with linear deterministic and stochastic It\^o perturbations. The existence of nonnegative weak martingale solutions on the semi-axis is established, and their asymptotic behavior as $t \to…

We prove existence of weak solutions to the obstacle problem for semilinear wave equations (including the fractional case) by using a suitable approximating scheme in the spirit of minimizing movements. This extends the results in [9],…

This paper proposes a novel particle scheme that provides convergent approximations of a weak solution of the Navier-Stokes equations for the 1-D flow of a viscous compressible fluid. Moreover, it is shown that all differential inequalities…

We consider a space-fractional wave equation with a singular mass term depending on the position and prove that it is very weak well-posed. The uniqueness is proved in some appropriate sense. Moreover, we prove the consistency of the very…

We prove existence of weak solutions (in the probabilistic sense) for a general class of stochastic semilinear wave equations on bounded domains of $R^d$ driven by a possibly discontinuous square integrable martingale.

In this paper we consider a fractional wave equation for hypoelliptic operators with a singular mass term depending on the spacial variable and prove that it has a very weak solution. Such analysis can be conveniently realised in the…

In this paper, we state with a variational method a general theorem providing the existence of a weak solution $u$ for fractional Euler-Lagrange equations of the type: $$ \dfrac{\partial L}{\partial x} (u,D^\alpha_- u,t) + D^\alpha_+…

This paper is concerned with an elliptic system of Kirchhoff type, driven by the variable-order fractional $p(x)$-operator. With the help of the direct variational method and Ekeland variational principle, we show the existence of a weak…

We propose a fully discrete variational scheme for nonlinear evolution equations with gradient flow structure on the space of finite Radon measures on an interval with respect to a generalized version of the Wasserstein distance with…

Wasserstein gradient flows provide a powerful means of understanding and solving many diffusion equations. Specifically, Fokker-Planck equations, which model the diffusion of probability measures, can be understood as gradient descent over…