Related papers: Asymptotic expansions for anisotropic heat kernels

Let $\mathbf{X}=\{X_t\}_{t\geq 0}$ be a L\'evy process in $\mathbb{R}^d$ and $\Omega$ be an open subset of $\mathbb{R}^d$ with finite Lebesgue measure. In this article we consider the quantity $H(t)=\int_{\Omega} \mathbb{P}^x…

We study the asymptotic expansion of the log-partition function of the anisotropic Heisenberg model in a bounded domain as this domain is dilated to infinity. Using the Ginibre's representation of the anisotropic Heisenberg model as a gas…

We show that, on a complete, connected and non-compact Riemannian manifold of non-negative Ricci curvature, the solution to the heat equation with $L^{1}$ initial data behaves asymptotically as the mass times the heat kernel. In contrast to…

We study the asymptotic behavior of solutions to the heat equation in nonhomogeneous media with critical singular density $$ |x|^{-2}\partial_{t}u=\Delta u, \quad \hbox{in} \ \real^N\times(0,\infty). $$ The asymptotic behavior proves to…

This paper is twofold. The first part aims to study the long-time asymptotic behavior of solutions to the heat equation on Riemannian symmetric spaces $G/K$ of noncompact type and of general rank. We show that any solution to the heat…

We study the relationship between the geometry and the Laplace spectrum of a Riemannian orbifold O via its heat kernel; as in the manifold case, the time-zero asymptotic expansion of the heat kernel furnishes geometric information about O.…

We give sharp conditions for the large time asymptotic simplification of aggregation-diffusion equations with linear diffusion. As soon as the interaction potential is bounded and its first and second derivatives decay fast enough at…

We study the small-time asymptotics of the heat content of smooth non-characteristic domains of a general rank-varying sub-Riemannian structure, equipped with an arbitrary smooth measure. By adapting to the sub-Riemannian case a technique…

By applying the covariant Taylor expansion method, the fifth lower coefficients the asymptotic expansion of the heat kernel associated with a fermion of spin 1/2 in Riemann-Cartan space are manifestly given. These coefficients in…

The method which allows for asymptotic expansion of the one-loop effective action W=ln det A is formulated. The positively defined elliptic operator A= U + M^2 depends on the external classical fields taking values in the Lie algebra of the…

In this paper we analyze the small-t asymptotic expansion of the trace of the heat kernel associated with a Laplace operator endowed with a spherically symmetric polynomially confining potential on the unbounded, d-dimensional Euclidean…

The aim of this paper is threefold. First, we obtain the precise bounds for the heat kernel on isotropic Heisenberg groups by using well-known results in the three dimensional case. Second, we study the asymptotic estimates at infinity for…

This paper is concerned with a nonlinear integral equation $$ (P)\qquad u(x,t)=\int_{{\bf R}^N}G(x-y,t)\varphi(y)dy+\int_0^t\int_{{\bf R}^N}G(x-y,t-s)f(y,s:u)dyds, \quad $$ where $N\ge 1$, $\varphi\in L^\infty({\bf R}^N)\cap L^1({\bf…

In this paper, we consider the asymptotic profiles of zero points for the spatial variable of the solutions to the heat equation. By giving suitable conditions for the initial data, we prove the existence of zero points by extending the…

We establish some asymptotic expansions for infinite weighted convolutions of distributions having light subexponential tails. Examples are presented, some showing that in order to obtain an expansion with two significant terms, one needs…

The high temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel…

Considered herein are the family of nonlinear equations with both dispersive and dissipative homogeneous terms appended. Solutions of these equations that start with finite energia decay to zero as time goes to infinity. We present an…

The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients…

We consider Dirichlet heat kernel $p_a^{(\mu)}(t,x,y)$ for the Bessel differential operator $L^{(\mu)}=\frac{d^2}{dx^2}+\frac{2\mu+1}{2x}$, $\mu\in\mathbb{R}$, in half-line $(a,\infty)$, $a>0$, and provide its asymptotic expansions for…

Let $H_h = h^2 L +V$ where $L$ is a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold and $V$ is a symmetric endomorphism field. We derive an asymptotic expansion for the heat kernel…