Related papers: Should we solve Plateau's problem again?

We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamiltonian, prove the solutions are unique, and prove that the…

In this work we investigate lump-like solutions in models described by a single real scalar field. We start considering non-topological solutions with the usual lump-like form, and then we study other models, where the bell-shape profile…

We describe a novel technique for solving the Plateau problem for constant curvature hypersurfaces based on recent work of Harvey and Lawson. This is illustrated by an existence theorem for hypersurfaces of constant Gaussian curvature in…

For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.

A non-linear theory for the plastic deformation of prismatic bodies is constructed which interpolates between Prandtl's linear soap-film approximation and N\'adai's sand-pile model . Geometrically Prandtl's soap film and N\'adai's wavefront…

We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the…

We give existence and nonuniqueness results for simple planar curves with prescribed geodesic curvature.

Surface bubbles are present in many industrial processes and in nature, as well as in CO$_2$ beverage. They have motivated many theoretical, numerical and experimental works. This paper presents the current knowledge on the physics of…

Building on work of Du, Gao, and Yau, we give a characterization of smooth solutions, up to normalization, of the complex Plateau problem for strongly pseudoconvex Calabi--Yau CR manifolds of dimension $2n-1 \ge 5$ and in the hypersurface…

The usable limits of the customary and relaxational filtrational theories are considered. The questions of applicable the locality and local thermodynamical equilibrium principles to depict the nonstationary flows are discussed. The…

This paper presents an analytical investigation of the solutions to a control volume model for liquid films flowing down a vertical fibre. The evolution of the free surface is governed by a coupled system of degenerate nonlinear partial…

This short review is devoted to the simple process of drying a multi-component droplet consisting of a complex fluid containing a salt. These processes provide a fascinating subject for study. The explanation of the rich variety of patterns…

In this paper we use the deformation procedure introduced in former work on deformed defects to investigate several new models for real scalar field. We introduce an interesting deformation function, from which we obtain two distinct…

In this paper, we mainly introduce a general method to study the existence and uniqueness of solution of free boundary problems with partially degenerate diffusion.

The present study aims to investigate the motion of buoyant rings in vertical soap films. Thickness differences and related bi-dimensional densities are considered as the motor leading to bi-dimensional buoyancy. We show how this effect can…

We try to find some exact analytical models of spherically symmetric spacetime of collapsing fluid under shearfree condition. We consider two types of solutions: one is to impose a condition on the mass function while the other is to…

Local oscillatory and other properties of source-type solutions of doubly nonlinear sixth-order parabolic thin film equations are studied.

In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin film peeled away from a substrate. The system underlying the process couples the weakly…

Motivated by the study of the equilibrium equations for a soap film hanging from a wire frame, we prove a compactness theorem for surfaces with asymptotically vanishing mean curvature and fixed or converging boundaries. In particular, we…

We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to achieve a rigorous understanding of the contact-angle…