Related papers: Heat content asymptotics for spectral boundary con…
The current study investigates the asymptotic spectral properties of a finite difference approximation of nonlocal Helmholtz equations with a Caputo fractional Laplacian and a variable coefficient wave number $\mu$, as it occurs when…
We consider a quantum graph where the operator contains a potential. We show that this operator admits a heat kernel. Under some assumptions on the potential, this heat kernel admits an asymptotic expansion at t=0 with coefficients that…
In this paper, we study large-time asymptotics for heat and fractional heat equations in two discrete settings: the full lattice \(\mathbb Z^d\) and finite connected subgraphs with Dirichlet boundary condition. These results provide a…
A review is presented of some recent progress in spectral geometry on manifolds with boundary: local boundary-value problems where the boundary operator includes the effect of tangential derivatives; application of conformal variations and…
We consider the asymptotics of the discrete heat kernel on isoradial graphs for the case where the time and the edge lengths tend to zero simultaneously. Depending on the asymptotic ratio between time and edge lengths, we show that two…
We study the heat content function, the heat trace function, and questions of isospectrality for the Laplacian with Dirichlet boundary conditions on a compact manifold with smooth boundary in the context of finite coverings and warped…
This is a mini-review of the heat kernel expansion for generalized Laplacians on various noncommutative spaces. Applications to the spectral action principle, renormalization of noncommutative theories and anomalies are also considered.
This letter is devoted to results on intermediate asymptotics for the heat equation. We study the convergence towards a stationary solution in self-similar variables. By assuming the equality of some moments of the initial data and of the…
We establish the two-term spectral asymptotics for boundary value problems of linear elasticity on a smooth compact Riemannian manifold of arbitrary dimension. We also present some illustrative examples and give a historical overview of the…
We study the weighted heat trace asymptotics of an operator of Laplace type with mixed boundary conditions where the weight function exhibits radial blowup. We give formulas for the first three boundary terms in the expansion in terms of…
In this paper we investigate the small time heat kernel asymptotics on the cut locus on a class of surfaces of revolution, which are the simplest 2-dimensional Riemannian manifolds different from the sphere with non trivial cut-conjugate…
We study the heat kernel for an operator of Laplace type with a $\delta$-function potential concentrated on a closed surface. We derive the general form of the small $t$ asymptotics and calculate explicitly several first heat kernel…
In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is analyzed in the usual set-up for dynamical systems generated by differential equations with delay terms. This approach is…
In this work a discontinuous boundary-value problem with retarded argument which contains spectral parameter in the transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues…
We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lp-spaces. We mainly address two model examples. In the first one, the diffusivity is of order two…
The asymptotic behavior of three-body scattering wave functions in configuration space is studied by considering a model equation that has the same asymptotic form as the Faddeev equations. Boundary conditions for the wave function are…
Asymptotically exact low temperature expansions for the $s=1/2$ Heisenberg XXZ chains with boundaries are implemented by using the boundary conformal field theory. It is found that for $1/2<\Delta\leq 1$, ($\Delta$, an anisotropic…
This paper aims to study the asymptotic behaviour of the fundamental solutions (heat kernels) of non-local (partial and pseudo differential) equations with fractional operators in time and space. In particular, we obtain exact asymptotic…
We consider the short time asymptotics of the heat content $E$ of a domain $D$ of $\mathbb{R}^d$. The novelty of this paper is that we consider the situation where $D$ is a domain whose boundary $\partial D$ is a random Koch type curve.…
We study properties of spectral minimal partitions of metric graphs within the framework recently introduced in [Kennedy et al, Calc. Var. 60 (2021), 61]. We provide sharp lower and upper estimates for minimal partition energies in…