Related papers: Vector-valued heat equations and networks with cou…
We study 3-dimensional gravity on a spacetime bounded by a generic 2-dimensional causal surface. We review the solution phase space specified by 4 generic functions over the causal boundary, construct the symplectic form over the solution…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
In the referred paper("H. Karani, C. Huber, Physical Review E, 91(2)(2015) 023304"), a total heat flux continuity condition for conjugate heat transfer problems with moving interfaces was proposed. The authors asserted both conductive and…
We study diffusions, variational principles and associated boundary value problems on directed graphs with natural weightings. Using random walks and exit times, we associate to certain subgraphs (domains) a pair of sequences, each of which…
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 consider initial-boundary value problems (IBVPs) on a finite interval for the system of the energy balance equation and Guyer-Krumhansl constitutive equation. Boundary conditions comprise various models of behavior of a physical system…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
We consider the inverse problem of finding matrix valued edge or nodal quantities in a graph from measurements made at a few boundary nodes. This is a generalization of the problem of finding resistors in a resistor network from voltage and…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
We study a free interface problem related to combustion of condensed matter and some non-equilibrium exothermal phase transitions. In spite of a variety of non-trivial dynamical scenarios exhibited by the model the solutions are uniformly…
We consider three-dimensional statistical systems at phase coexistence in the half-volume with boundary conditions leading to the presence of an interface. Working slightly below the critical temperature, where universal properties emerge,…
We consider the problem of existence of a solution $u$ to $\partial_t u-\partial_{xx} u = 0$ in $(0,T)\times\mathbb{R}_+$ subject to the boundary condition $-u_x(t,0)+g(u(t,0))=\mu$ on $(0,T)$ where $\mu$ is a measure on $(0,T)$ and $g$ a…
We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamical systems, as well as in systems modeling the dynamical…
A nonlinear divergence parabolic equation with dynamic boundary conditions of Wentzell type is studied. The existence and uniqueness of a strong solution is obtained as the limit of a finite difference scheme, in the time dependent case and…
In this paper we study a semilinear hyperbolic-parabolic system as a model for some chemotaxis phenomena evolving on networks; we consider transmission conditions at the inner nodes which preserve the fluxes and non- homogeneous boundary…
This work deals with an inverse boundary value problem arising from the equation of heat conduction. We reconstruct small perturbations of the (isotropic) heat conductivity distribution from partial (on accessible part of the boundary)…
This paper tests a dielectric model for variation of hydration free energy with geometry of complex solutes in water. It works out some basic aspects of the theory of boundary integral methods for these problems. One aspect of the…
Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary…
Complex natural or engineered systems comprise multiple characteristic scales, multiple spatiotemporal domains, and even multiple physical closure laws. To address such challenges, we introduce an interface learning paradigm and put forth a…
In this paper, we show that a hybrid method using coupled boundary measurements can determine electrical conductivity, thermal conductivity, and the product of heat capacity and heat density within a bounded domain on the plane uniquely up…