Related papers: Heat trace asymptotics with singular weight functi…
In this article we study transition probabilities of a class of subordinate Brownian motions. Under mild assumptions on the Laplace exponent of the corresponding subordinator, sharp two sided estimates of the transition probability are…
The spectral heat content is investigated for time-changed killed Brownian motions on C1,1 open sets, where the time change is given by either a subordinator or an inverse subordinator, with the underlying Laplace exponent being regularly…
Our topological setting is a smooth compact manifold of dimension two or higher with smooth boundary. Although this underlying topological structure is smooth, the Riemannian metric tensor is only assumed to be bounded and measurable. This…
We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading…
We obtain an off-diagonal upper bound for Green and heat kernel of Laplace type operator on symmetric spaces.
In this paper, we study the formation of finite time singularities for the solution of the boundary layer equations in the two-dimensional incompressible heat conducting flow. We obtain that the first spacial derivative of the solution…
We study the heat content for Laplacians on compact, finite metric graphs with Dirichlet conditions imposed at the "boundary" (i.e., a given set of vertices). We prove a closed formula of combinatorial flavour, as it is expressed as a sum…
For parabolic spatially discrete equations, we consider Green's functions, also known as heat kernels on lattices. We obtain their asymptotic expansions with respect to powers of time variable $t$ up to an arbitrary order and estimate the…
Given a cone pseudodifferential operator $P$ we give a full asymptotic expansion as $t\to 0^+$ of the trace $\Tr Pe^{-tA}$, where $A$ is an elliptic cone differential operator for which the resolvent exists on a suitable region of the…
In this article we determine the Laplace transforms of the main boundary functionals of the oscillating compound Poisson process. These are the first passage time of the level, the joint distribution of the first exit time from the interval…
We study the heat kernel for a Laplace type partial differential operator acting on smooth sections of a complex vector bundle with the structure group $G\times U(1)$ over a Riemannian manifold $M$ without boundary. The total connection on…
Boundary conformal field theories have several additional terms in the trace anomaly of the stress tensor associated purely with the boundary. We constrain the corresponding boundary central charges in three- and four-dimensional conformal…
The asymptotics of a singularly perturbed problem is constructed. describing the transport of a polydisperse impurity in the atmosphere, taking into account the processes of precipitation and wind pick-up, as well as the processes of…
An analytic solution to a stationary heat conduction problem in 2D unbounded doubly periodic composite materials with temperature dependent conductivities of their components is given. Corresponding nonlinear boundary value problem is…
We study the asymptotic behavior of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions imposing Robin boundary conditions. Assuming the existence of…
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…
In this work, we study the asymptotic behaviour of solutions to the heat equation in exterior domains, i.e., domains which are the complement of a smooth compact set in $\mathbb{R}^N$. Different homogeneous boundary conditions are…
We study temperature distribution in a heat conducting problem, for a system of p-Laplace equation, giving rise to a free boundary.
We consider the heat-kernel expansion of the massive Laplace operator on the three dimensional ball with Dirichlet boundary conditions. Using this example, we illustrate a very effective scheme for the calculation of an (in principle)…
The heat trace asymptotics on the noncommutative torus, where generalized Laplacians are made out of left and right regular representations, is fully determined. It turns out that this question is very sensitive to the number-theoretical…