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

Well-posedness of a free boundary problem for electrostatic microelectromechanical systems (MEMS) is investigated when nonlinear bending effects are taken into account. The model describes the evolution of the deflection of an electrically…

A nonlinear Poisson--Boltzmann equation with transmission boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic…

We study degenerate fully nonlinear free transmission problems, where the degeneracy rate varies in the domain. We prove optimal pointwise regularity depending on the degeneracy rate. Our arguments consist of perturbation methods, relating…

In the class of the so called non-dynamic Fractional Obstacle Problems of parabolic type, it is shown how to obtain higher regularity as well as optimal regularity of the space derivatives of the solution. Furthermore, at free boundary…

We consider the dynamics of an electrostatically actuated thin elastic plate being clamped at its boundary above a rigid plate. The model includes the harmonic electrostatic potential in the three-dimensional time-varying region between the…

We analyze the thermodynamics of the focusing discrete nonlinear Schr\"odinger equation in dimensions $d\ge 3$ with general nonlinearity $p>1$ and under a model with two parameters, representing inverse temperature and strength of the…

A classical topic in the mathematical theory of hydrodynamics is to study the evolution of the free surface separating air from an incompressible perfect fluid. The goal of this survey is to examine this problem for two important sets of…

This is the sequel of the recent work (Du, Huang, Pu, Commun. Math. Phys, 2023, doi: 10.1007/s00220-023-04651-7) on axially symmetric gravity water waves with general vorticities, which has investigated the singular wave profile of the free…

An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward…

We provide a description of phase transitions at finite temperature in strongly coupled field theories using holography. For this purpose, we introduce a general class of gravity duals to superconducting theories that exhibit various types…

Using inhomogeneous dynamical mean-field theory, we argue that the normal-metal proximity effect forces any finite number of "barrier" planes that are described by the (paramagnetic) Hubbard model and sandwiched between semi-infinite…

We consider a simplified model of a two-phase flow through a heterogeneous porous medium, in which the convection is neglected. This leads to a nonlinear degenerate parabolic problem in a domain shared in an arbitrary finite number of…

This paper deals with regularity theory for two-phase free boundary variational problems ruled by degenerate elliptic operators.

In the area of topological and geometric treatment of phase transitions and symmetry breaking in Hamiltonian systems, in a recent paper some general sufficient conditions for these phenomena in $\mathbb{Z}_2$-symmetric systems (i.e.…

We consider structure of a thermal phase-slip center for a simple microscopic model of a clean one-dimensional superconductors in which superconductivity occurs only within one conducting channel or several identical channels. Surprisingly,…

In this paper, we prove the maximal $L_p$-$L_q$ regularity of the compressible and incompressible two phase flow with phase transition in the model problem case with the help of ${\mathcal R}$-bounded solution operators corresponding to…

A two-dimensional free boundary transmission problem arising in the modeling of an electrostatically actuated plate is considered and a representation formula for the derivative of the associated electrostatic energy with respect to the…

We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…

We formulate and study a variational two-phase free boundary problem with Robin condition on the interface between the two phases, and we prove existence and regularity of solutions in dimension two

We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space which evolve by an arbitrary (non-homogeneous) function of the radii of curvature. The associated flow of the radii of…