Related papers: Heat content

We obtain pointwise lower bounds for heat kernels of higher order differential operators with Dirichlet boundary conditions on bounded domains in $\R^N$. The bounds exhibit explicitly the nature of the spatial decay of the heat kernel close…

In this paper, we observe how the heat equation in a non-cylindrical domain can arise as the asymptotic limit of a parabolic problem in a cylindrical domain, by adding a potential that vanishes outside the limit domain. This can be seen as…

This paper establishes the precise small-time asymptotic behavior of the spectral heat content for isotropic L\'evy processes on bounded $C^{1,1}$ open sets of $\mathbb{R}^{d}$ with $d\ge 2$, where the underlying characteristic exponents…

For incomplete sub-Riemannian manifolds, and for an associated second-order hypoelliptic operator, which need not be symmetric, we identify two alternative conditions for the validity of Gaussian-type upper bounds on heat kernels and…

We study a parabolic free boundary problem, arising from a model for the propagation of equi-diffusional premixed flames with high activation energy. If an initial data is compactly supported, then the solution vanishes in a finite time,…

In this paper we study the asymptotic behavior, as $t\downarrow 0$, of the spectral heat content $Q^{(\alpha)}_{D}(t)$ for isotropic $\alpha$-stable processes, $\alpha\in [1,2)$, in bounded $C^{1,1}$ open sets $D\subset \R^{d}$, $d\geq 2$.…

We derive the macroscopic laws that govern the evolution of the density of particles in the exclusion process on the Sierpinski gasket in the presence of a variable speed boundary. We obtain, at the hydrodynamics level, the heat equation…

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 study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the…

We study the heat equation on a half-space or on an exterior domain with a linear dynamical boundary condition. Our main aim is to establish the rate of convergence to solutions of the Laplace equation with the same dynamical boundary…

Let $(M^n, g)$ be a complete Riemannian manifold with $Rc\geq -Kg$, $H(x, y, t)$ is the heat kernel on $M^n$, and $H= (4\pi t)^{-\frac{n}{2}}e^{-f}$. Nash entropy is defined as $N(H, t)= \int_{M^n} (fH) d\mu(x)- \frac{n}{2}$. We studied the…

We obtain two-sided heat kernel estimates for Riemannian manifolds with ends with mixed boundary condition, provided that the heat kernels for the ends are well understood. These results extend previous results of Grigor'yan and…

We consider steady-state diffusion in a bounded planar domain with multiple small targets on a smooth boundary. Using the method of matched asymptotic expansions, we investigate the competition of these targets for a diffusing particle and…

We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the $\sqrt{t}$-behavior of…

The principal aim of this short note is to extend a recent result on Gaussian heat kernel bounds for self-adjoint $L^2(\Om; d^n x)$-realizations, $n\in\bbN$, $n\geq 2$, of divergence form elliptic partial differential expressions $L$ with…

We study qualitative properties of initial traces of nonnegative solutions to a semilinear heat equation in a smooth domain under the Dirichlet boundary condition. Furthermore, for the corresponding Cauchy--Dirichlet problem, we obtain…

We consider a general second-order elliptic differential operator on a domain with a cylindrical end. We impose Dirichlet boundary conditions on the boundary with the exception of a small set, where we impose Neumann boundary conditions.…

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…

In this note we consider achieving the largest principle eigenvalue of a Robin Laplacian on a bounded domain $\Omega$ by optimizing the Robin parameter function under an integral constraint. The main novelty of our approach lies in…

For a sub-Riemannian manifold provided with a smooth volume, we relate the small time asymptotics of the heat kernel at a point $y$ of the cut locus from $x$ with roughly "how much" $y$ is conjugate to $x$. This is done under the hypothesis…