Related papers: Finite time singularity in a free boundary problem…
The relativistic membrane equation can be rewritten as a first order hyperbolic system. Making use of the characteristic decomposition method, a new blow-up theorem is established. As an application, it demonstrates the formation of…
We establish the first complete classification of finite-time blow-up scenarios for strong solutions to the three-dimensional incompressible Euler equations with surface tension in a bounded domain possessing a closed, moving free boundary.…
In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…
To enable the study of criticality in multicomponent fluids, the standard spherical model is generalized to describe an $\ns$-species hard core lattice gas. On introducing $\ns$ spherical constraints, the free energy may be expressed…
In this paper, the authors consider an initial boundary value problem for the heat flow of equation of surfaces with constant mean curvatures, which was investigated in [On the heat flow of equation of surfaces of constant mean curvatures,…
We investigate the impact of singularities occurring at future times in solutions of the Friedmann equations expressed in conformal coordinates. We focus on the consequences of extending the time coordinate through the singularity for the…
We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in [9], wherein the…
We study a quantum Hot Big Bang in the connection representation, with a matter constant of motion m whose conjugate defines time. Superpositions in m induce a unitary inner product. The wavefunction reveals a resolution of the singularity…
This paper deals with the quasilinear parabolic-elliptic chemotaxis system with logistic source and nonlinear production, \begin{equation*} \begin{cases} u_t=\nabla \cdot (D(u) \nabla u) - \nabla \cdot (S(u)\nabla v) + \lambda u - \mu…
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods (MFEM) in space for simulating…
We discuss the influence of white noise on a generic dynamical finite-time-singularity model for a single degree of freedom. We find that the noise effectively resolves the finite-time-singularity and replaces it by a first-passage-time or…
We construct the first example of finite time blow-up solutions for the heat flow of the $H$-system, describing the evolution of surfaces with constant mean curvature \begin{equation*} \left\{ \begin{aligned} &u_t = \Delta u -…
We consider a well-known model for micro-electromechanical systems (MEMS) with variable dielectric permittivity, based on a parabolic equation with singular nonlinearity. We study the touchdown or quenching phenomenon. Recently, the…
Under mean curvature flow, a closed, embedded hypersurface $M(t)$ becomes singular in finite time. For certain classes of mean-convex mean curvature flows, we show the continuity of the first singular time $T$ and the limit set "$M(T)$",…
We consider a fourth order, reaction-diffusion type, singularly perturbed boundary value problem, and the regularity of its solution. Specifically, we provide estimates for arbitrary order derivatves, which are explicit in the singular…
A finite-time fluctuation theorem is proved for the diffusion-influenced surface reaction A<->B in a domain with any geometry where the species A and B undergo diffusive transport between the reservoir and the catalytic surface. A…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
In this paper we study the existence, the optimal regularity of solutions, and the regularity of the free boundary near the so-called \emph{regular points} in a thin obstacle problem that arises as the local extension of the obstacle…
We investigate a class of free boundary problems with oscillatory singularities within stochastic materials. Our main result yields sharp regularity estimates along the free boundary, provided the power of the singularity varies in a…
The problem of electromagnetic scattering by cylinders is an old problem that has been studied in many configurations. The present publication provides a theoretical study on a not yet investigated general case: the set of finite metallic…