相关论文: Intermediate Asymptotics of the Capillary-Driven T…
The paper focuses on a model describing the spreading of an insoluble surfactant on a thin viscous film with capillary effects taken into account. The governing equation for the film height is degenerate parabolic of fourth order and…
It is shown that a Riemann-type problem with discontinuous data of sign-type for the thin film equation, which degenerates at +1 and -1, admits a self-similar solution. Both FBP and the Cauchy problem (oscillatory solutions near interfaces)…
The problem of diffraction of a waveguide mode by a thin Neumann screen is considered. The incident mode is assumed to have frequency close to the cut-off. The problem is reduced to a propagation problem on a branched surface and then is…
We study a class of lubrication-type equations modeling the spread of thin poroelastic biofilms at air/agar interfaces. Starting from a biofilm slab model, we perform a formal multi-scale asymptotic expansion to derive a reduced nonlinear…
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…
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…
We study the long-time behavior of localized solutions to linear or semilinear parabolic equations in the whole space $\mathbb{R}^n$, where $n \ge 2$, assuming that the diffusion matrix depends on the space variable $x$ and has a finite…
The question is studied whether weak solutions of linear partial integrodifferential equations approach a constant spatial profile after rescaling, as time goes to infinity. The possible limits and corresponding scaling functions are…
In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…
We derive an exact closed-form representation for the Euclidean thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space. This can be interpreted as the real part of a complex analytic function of a…
This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or…
A number of commercial fluids, including synthetic automotive oils, food and consumer products containing polymer additives exhibit weakly rate-thickening responses in the final stages of capillarity-driven thinning, where a large…
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…
This letter is devoted to results on intermediate asymptotics for the heat equation. We study the convergence towards a stationary solution in self-similar variables. By assuming the equality of some moments of the initial data and of the…
Interface equations are derived for both binary diffusive and binary fluid systems subjected to non-equilibrium conditions, starting from the coarse-grained (mesoscopic) models. The equations are used to describe thermo-capillary motion of…
We study the short-time dynamics of a liquid ligament, held between two solid cylinders, when one is impulsively accelerated along its axis. A set of one-dimensional equations in the slender-slope approximation is used to describe the…
The main results of this article provide asymptotics at infinity of the Green's functions near and at the spectral gap edges for "generic" periodic second-order elliptic operators on noncompact Riemannian co-compact coverings with abelian…
We consider the problem of wave propagation for a 2-D rectilinear optical waveguide which presents some perturbation. We construct a mathematical framework to study such a problem and prove the existence of a solution for the case of small…
We study an elliptic equation with measurable coefficients arising from photo-acoustic imaging in inhomogeneous media. We establish Holder continuity of weak solutions and obtain pointwise bounds for Green's functions subject to Dirichlet…
We consider an initial-boundary value problem for a class of nonlocal thin film equations governed by the spectral fractional Laplacian with homogeneous Neumann boundary conditions. We were the first to establish an $\alpha$-entropy…