Related papers: Uniform asymptotic formulae for Green's kernels in…
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 local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet boundary condition. Our analysis is based on a blow-up procedure which involves some Almgren type…
We derive upper bounds for the trace of the heat kernel $Z(t)$ of the Dirichlet Laplace operator in an open set $\Omega \subset \R^d$, $d \geq 2$. In domains of finite volume the result improves an inequality of Kac. Using the same methods…
A subordinate Brownian motion $X$ is a L\'evy process which can be obtained by replacing the time of the Brownian motion by an independent subordinator. In this paper, when the Laplace exponent $\phi$ of the corresponding subordinator…
We study the asymptotic behavior of the solutions related to a family of singularly perturbed linear partial differential equations in the complex domain. The analytic solutions obtained by means of a Borel-Laplace summation procedure are…
We consider a 2-dimensional thin domain with order of thickness {\epsilon} which presents oscillations of amplitude also {\epsilon} on both boundaries, top and bottom, but the period of the oscillations are of different order at the top and…
A mixed Dirichlet-Neumann problem is regularized with a family of singularly perturbed Neumann-Robin boundary problems, parametrized by $\varepsilon > 0$. Using an asymptotic development by Gamma-convergence, the asymptotic behavior of the…
The Brownian motion over the space of fluid velocity configurations driven by the hydrodynamical equations is considered. The Green function is computed in the form of an asymptotic series close to the standard diffusion kernel. The high…
In this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type $R^\epsilon = \{(x,y) \in \R^2; x \in (0,1), 0 < y < \epsilon G(x, x/\epsilon)\} $ where the function G(x,y) is…
We develop an asymptotic analysis of target fluxes in the three-dimensional (3D) narrow capture problem. The latter concerns a diffusive search process in which the targets are much smaller than the size of the search domain. The small…
We consider a singularly perturbed Dirichlet spectral problem for an elliptic operator of second order. The coefficients of the operator are assumed to be locally periodic and oscillating in the scale $\varepsilon$. We describe the leading…
We study a family of singularly perturbed $q-$difference-differential equations in the complex domain. We provide sectorial holomorphic solutions in the perturbation parameter $\epsilon$. Moreover, we achieve the existence of a common…
We present a new complexification scheme based on the classical double layer potential for the solution of the Helmholtz equation with Dirichlet boundary conditions in compactly perturbed half-spaces in two and three dimensions. The kernel…
In this paper, we study existence, uniqueness and asymptotic behavior of the Laplace equation with dynamical boundary conditions on regular non-cylindrical domains. We write the problem as a non-autonomous Dirichlet-to-Neumann operator and…
We deal with a singularly perturbed optimal control problem with slow and fast variable depending on a parameter {\epsilon}. We study the asymptotic, as {\epsilon} goes to 0, of the corresponding value functions, and show convergence, in…
We describe a new Maple package for treating boundary problems for linear ordinary differential equations, allowing two-/multipoint as well as Stieltjes boundary conditions. For expressing differential operators, boundary conditions, and…
Let $\omega\subset\mathbb{R}^n$ be a bounded domain with Lipschitz boundary. For $\varepsilon>0$ and $n\in\mathbb{N}$ consider the infinite cone $\Omega_{\varepsilon}:=\big\{(x_1,x')\in (0,\infty)\times\mathbb{R}^n: x'\in\varepsilon…
In this contribution we present an overview of our work on the numerical simulation of the perturbation of a black hole space-time by incoming gravitational waves. The formulation we use is based on Friedrich's general conformal equations…
We study pointwise behavior of positive solutions to nonlinear integral equations, and related inequalities, of the type \begin{equation*} u(x) - \int_\Omega G(x, y) \, g(u(y)) d \sigma (y) = h, \end{equation*} where $(\Omega, \sigma)$ is a…
The analytic and formal solutions to a family of singularly perturbed partial differential equations in the complex domain involving two complex time variables are considered. The analytic continuation properties of the solution of an…