Related papers: Temperature on rods with Robin boundary conditions

We consider a semi-infinite one-dimensional phase-change material with two unknown constant thermal coefficients among the latent heat per unit mass, the specific heat, the mass density and the thermal conductivity. Aiming at the…

Liouville theorems for scaling invariant nonlinear parabolic problems in the whole space and/or the halfspace (saying that the problem does not posses positive bounded solutions defined for all times $t\in(-\infty,\infty)$) guarantee…

Let $(M,g)$ be a two-dimensional Riemannian manifold of finite diameter with a conical singularity. Under the assumption that the metric near the cone point $C$ is rotationally invariant, but not necessarily flat, we give an explicit…

We study Schroedinger operators with Robin boundary conditions on exterior domains in $\R^d$. We prove sharp point-wise estimates for the associated semi-groups which show, in particular, how the boundary conditions affect the time decay of…

For $p\in (1,+\infty)$ and $b \in (0, +\infty]$ the $p$-torsion function with Robin boundary conditions associated to an arbitrary open set $\Om \subset \R^m$ satisfies formally the equation $-\Delta_p =1$ in $\Om$ and $|\nabla u|^{p-2}…

The heat transfer model for a one-dimensional supercooled melt during the final stage of solidification is considered. The Stefan problem for the determination of the temperature distribution is solved under the condition that (i) the…

It is argued that the specific heat of amorphous solids at low temperatures can be understood to arise from a single branch of collective modes. The idea is illustrated in a model of a correlated spin glass for which magnetic anisotropies…

Let $M$ be a Riemannian manifold and $\Omega$ a smooth domain of $M$. We study the following heat diffusion problem: assume that the initial temperature is equal to $1$, uniformly on $\Omega$, and is $0$ on its complement. Heat will then…

We obtain explicit expressions for one unknown thermal coefficient (among the conductivity, mass density, specific heat and latent heat of fusion) of a semi-infinite material through the one-phase fractional Lam\'e-Clapeyron-Stefan problem…

A lagrangian for gauge fields coupled to fermions with the Kac-Moody group as its gauge group yields, for the pure fermions sector, an ideal gas of Kac-Moody fermions. The canonical partition function for the $\hat U(1)$ case is shown to…

We study an inverse parabolic problem of identifying two source terms in heat equation with dynamic boundary conditions from a final time overdetermination data. Using a weak solution approach by Hasanov, the associated cost functional is…

We present some new bounds for the first Robin eigenvalue with a negative boundary parameter. These include the constant volume problem, where the bounds are based on the shrinking coordinate method, and a proof that in the fixed perimeter…

The paper is concerned with a kind of minimal time control problem for the heat equation with impulse controls. The purpose of such a problem is to find an optimal impulse control (among certain control constraint set) steering the solution…

Given any $d$-dimensional Lipschitz Riemannian manifold $(M,g)$ with heat kernel $\mathsf{p}$, we establish uniform upper bounds on $\mathsf{p}$ which can always be decoupled in space and time. More precisely, we prove the existence of a…

We discuss the thermal behaviour of the pion vector form factors and calculate them in one-loop Chiral Perturbation Theory. The perturbative result is used to analyze the $T$-dependent electromagnetic pion charge radius, obtaining a rough…

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…

We estimate the heat kernel on a closed Riemannian manifold $M$, with $dim(M)\geq 3$, evolving under the Ricci-harmonic map flow and the result depends on some constants arising from a Sobolev imbedding theorem. In a special case, when the…

In this paper, we consider the fractional heat equation $u_{t}=\triangle^{\alpha/2}u+f(u)$ with Dirichlet boundary conditions on the ball $B_{R}\subset \mathbb{R}^{d}$, where $\triangle^{\alpha/2}$ is the fractional Laplacian,…

We study dynamic cooling, where an externally driven two-level system is cooled via reservoir, a quantum system with initial canonical equilibrium state. We obtain explicitly the minimal possible temperature $T_{\rm min}>0$ reachable for…

We give a proof of Gaussian upper bound for the heat kernel coupled with the Ricci ow. Previous proofs by Lei Ni [5] use Harnack inequality and doubling volume property, also the recent proof by Zhang and Cao [6] uses Sobolev type…