相关论文: A parabolic free transmission problem: flat free b…

In this paper we study regularity properties of the free boundary problem from superconductivity close to a fixed boundary. If the origin is a free boundary point, then we show that the free boundary touches the fixed boundary tangentially.

Using a direct approach, we prove a $2$-dimensional epiperimetric inequality for the one-phase problem in the scalar and vectorial cases and for the double-phase problem. From this we deduce, in dimension $2$, the $C^{1,\alpha}$ regularity…

We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open boundary…

This paper gives a 2D hamonic lattices model with missing bond defects, when the capacity ratio of defects is enough large, the temperature gradient can be formed and the finite heat conduction is found in the model. The defects in the 2D…

We prove existence and regularity results for free transmission problems governed by fully nonlinear elliptic equations with nonhomogeneous degeneracies.

In this paper a strongly degenerate parabolic equation derived from a density dependent particle flow model is studied. Furthermore, a free boundary problem and its connection to the strongly degenerate parabolic equation is investigated.…

We study the fundamental problem of two gas species in two dimensional velocity space whose molecules collide as hard circles in the presence of a flat boundary and with dependence on only one space dimension. The case of three-dimensional…

The paper presents a theoretical study using the Karman-Pohlhausen method for describing the transient heat exchange between the boundary-layer free convection and a vertical flat plate embedded in a porous medium. The unsteady behavior is…

The multistate Potts models on two-dimensional hyperbolic lattices are studied with respect to various boundary effects. The free energy is numerically calculated by Corner Transfer Matrix Renormalization Group method. We analyze phase…

Motivated by a new kind of initial boundary value problem (IBVP) with a free boundary arising in wave-structure interaction, we propose here a general approach to one-dimensional IBVP as well as transmission problems. For general strictly…

The existence, uniqueness, and asymptotic behavior of steady transonic flows past a curved wedge, involving transonic shocks, governed by the two-dimensional full Euler equations are established. The stability of both weak and strong…

The parabolic obstacle problem for the fractional Laplacian naturally arises in American option models when the assets prices are driven by pure jump L\'evy processes. In this paper we study the regularity of the free boundary. Our main…

We consider a two-dimensional generalization of the Su-Schrieffer-Heeger model which is known to possess a non-trivial topological band structure. For this model, which is characterized by a single parameter, the hopping ratio $0 \leq r\leq…

In this paper we consider a quasilinear elliptic PDE, $\text{div} (A(x,u) \nabla u) =0$, where the underlying physical problem gives rise to a jump for the conductivity $A(x,u)$, across a level surface for $u$. Our analysis concerns…

We consider the free boundary problem for relativistic plasma--vacuum interfaces in two and three spatial dimensions. The plasma flow is governed by the equations of ideal relativistic magnetohydrodynamics, while the vacuum magnetic and…

Over the past two decades, the controllability of several examples of parabolic-hyperbolic systems has been investigated. The present article is the beginning of an attempt to find a unified framework that encompasses and generalizes the…

We analyze the phase transitions of an interacting electronic system weakly coupled to free-electron leads by considering its zero-bias conductance. This is expressed in terms of two effective impurity models for the cases with and without…

We establish a C^1,alpha Schauder estimate of a non-standard degenerate elliptic equation and use it to give another proof of the higher order boundary Harnack inequality. As an application, we obtain the analyticity of the free boundary in…

We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but…

We consider parabolic equations with mixed boundary conditions and domain inhomogeneities supported on a lower dimensional hypersurface, enforcing a jump in the conormal derivative. Only minimal regularity assumptions on the domain and the…