Related papers: Heat content asymptotics for spectral boundary con…
We study the asymptotic behaviour of solutions of a class of linear non-local measure-valued differential equations with time delay. Our main result states that the solutions asymptotically exhibit a parabolic like behaviour in the large…
In this paper, we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. Namely, we show that, under broad assumptions, the first…
Equilibrium finite temperature observables of a CFT can be described by a local effective action for background fields -- a "thermal effective action." This effective action determines the asymptotic density of states of a CFT as a detailed…
In this paper we provide a characterization of sets of finite local and non local perimeter via a $\Gamma-$convergence result. As an application we give a proof of the isoperimetric inequality, both in the local and in the non local case.
We establish new asymptotic results for the solutions of the second-grade fluids equations and characterize their decay rate in terms of the behavior of the initial data. Moreover, assuming more regularity for the initial data, we study the…
In this paper we compute the coefficients of the heat kernel asymptotic expansion for Laplace operators acting on scalar functions defined on the so called spherical suspension (or Riemann cap) subjected to Dirichlet boundary conditions. By…
We consider the heat equation in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to an improvement of the decay rate of the heat…
The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…
We study the large-time behavior in all $L^p$ norms of solutions to an inhomogeneous nonlocal heat equation in $\mathbb{R}^N$ involving a Caputo $\alpha$-time derivative and a power $\beta$ of the Laplacian when the dimension is large, $N>…
We study the fifth term in the asymptotic expansion of the heat operator trace for a partial differential operator of Laplace type on a compact Riemannian manifold with Dirichlet or Neumann boundary conditions.
We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter…
Thermal instabilities can cause a radiative shock to oscillate, thereby modulating the emission from the post-shock region. The mode frequencies are approximately quantised in analogy to those of a vibrating pipe. The stability properties…
In this work we study the large-time behaviour of solutions of the Heat Equation in the hyperbolic space $\mathbb{H}^d$, providing precise speeds of convergence in $L^1$ and $L^\infty$ to their asymptotic profiles by means of an adaptation…
This paper deals with the problem of internal null-controllability of a heat equation posed on a bounded domain with Dirichlet boundary conditions and perturbed by a semilinear nonlocal term. We prove the small-time local…
We establish $L^2$-exponential decay properties for linear dissipative kinetic equations, including the time-relaxation and Fokker-Planck models, in bounded spatial domains with general boundary conditions that may not conserve mass. Their…
The magnetic susceptibility and the low-temperature specific heat of the 1-dimensional Hubbard model under the integrable open-boundary conditions are discussed through the Bethe ansatz with the string hypothesis. The contributions of the…
The purpose of this paper is to investigate the principal spectral theory and asymptotic behavior of the spectral bound for cooperative nonlocal dispersal systems, specifically focusing on the case where partial diffusion coefficients are…
We present preliminary experimental data that enable us to suggest that heat transfer in cellular tissue under local strong heating is a more complex phenomenon than a simple heat diffusion. Namely, we demonstrate that under local strong…
The non-extensive self-consistent theory describing the thermodynamics of hadronic systems at high temperatures is used to derive some thermodynamical quantities, as pressure, entropy, speed of sound and trace-anomaly. The calculations are…
We consider weak solutions of the fractional heat equation posed in the whole $n$-dimensional space, and establish their asymptotic convergence to the fundamental solution as $t\to\infty$ under the assumption that the initial datum is an…