Related papers: Sensitivity for Smoluchowski equation

Solutions to elliptic equations often exhibit higher regularity properties such as \emph{higher integrability}. That is, for instance, a solution $u$ to a system that a priori only satisfies $ u \in W^{1,r}$ is more regular and even in the…

Finitary/static semantics in the form of intersection type assignments have become a paradigm for analysing the fine structure of all sorts of lambda-models. The key step is the construction of a filter model isomorphic to a given…

This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with non-homogeneous smoothness across the domain. Two challenging issues that arise in this context are the evaluation…

In this paper, the theory of Gelfand problems is adapted to the 1--Laplacian setting. Concretely, we deal with the following problem \begin{equation*} \left\{\begin{array}{cc} -\Delta_1u=\lambda f(u) &\hbox{in }\Omega\,;\\[2mm] u=0…

In present paper, we study the normalized solutions $(\lambda_c, u_c)\in \R\times H^1(\R^N)$ to the following Kirchhoff problem $$ -\left(a+b\int_{\R^N}|\nabla u|^2dx\right)\Delta u+\lambda u=g(u)~\hbox{in}~\R^N,\;1\leq N\leq 3 $$…

We study the electric Helmholtz equation $\Delta u + Vu + \lambda u =f$ and show that, for certain potentials, the solution $u$ given by the limited absorption principle obeys a Sommerfeld radiation condition. We use a non-spherical…

We study the dynamic response of a Fermi liquid in the spin, charge and nematic channels beyond the random phase approximation for the dynamically screened Coulomb potential. In all the channels, one-loop order corrections to the…

Let $X$ be a (data) set. Let $K(x,y)>0$ be a measure of the affinity between the data points $x$ and $y$. We prove that $K$ has the structure of a Newtonian potential $K(x,y)=\varphi(d(x,y))$ with $\varphi$ decreasing and $d$ a quasi-metric…

Let $f \in M_+(\R_+)$, the class of nonnegative, Lebesgure-measurable functions on $\R_+=(0, \infty)$. We deal with integral operators of the form \[ (T_Kf)(x)=\int_{\R_+}K(x,y)f(y)\, dy, \quad x \in \R_+, \] with $K \in M_+(\R_+^2)$. We…

Let $X$ be a separable Banach space endowed with a non-degenerate centered Gaussian measure $\mu$. The associated Cameron-Martin space is denoted by $H$. Let $\nu=e^{-U}\mu$, where $e^{-U}$ is a sufficiently regular weight and…

We investigate the problem of pointwise convergence of the family of non-linear integral operators: \begin{equation} L_\lambda(f,x) = \int_a^b \sum_{m=1}^N f^m(t) K_{\lambda ,m}(x,t) dt, \end{equation} where $\lambda $ is a real parameters,…

We show that the solutions to the damped stochastic wave equation converge pathwise to the solution of a stochastic heat equation. This is called the Smoluchowski-Kramers approximation. Cerrai and Freidlin have previously demonstrated that…

We study the existence of normalized solutions to the following Choquard equation with $F$ being a Berestycki-Lions type function \begin{equation*} \begin{cases} -\Delta u+\lambda u=(I_{\alpha}\ast F(u))f(u),\quad \text{in}\ \mathbb{R}^N,…

I present a new approximation of the $S$-matrix dependence on momentum $q$, formulated as a sum of a rational function and a truncated Sinc series. This approach enables pointwise determination of the $S$ matrix with specified resolution,…

Given a strongly local Dirichlet space and $\lambda\geq 0$, we introduce a new notion of $\lambda$--subharmonicity for $L^1_\loc$--functions, which we call \emph{local $\lambda$--shift defectivity}, and which turns out to be equivalent to…

Consider the Cauchy problem for a strictly hyperbolic, $N\times N$ quasilinear system in one space dimension $$ u_t+A(u) u_x=0,\qquad u(0,x)=\bar u(x), \eqno (1) $$ where $u \mapsto A(u)$ is a smooth matrix-valued map, and the initial data…

We consider a reaction-diffusion equation of the type \[ \partial_t\psi = \partial^2_x\psi + V(\psi) + \lambda\sigma(\psi)\dot{W} \qquad\text{on $(0\,,\infty)\times\mathbb{T}$}, \] subject to a "nice" initial value and periodic boundary,…

We consider the equation u_t=\epsilon u_{xx}+(u\ K'*u)_x for x\in\mathbb{R}, t>0 and with \epsilon\geq 0, supplemented with a nonnegative, integrable initial datum. We present a class of interaction kernels K' such that the large time…

We consider self-similar solutions with finite mass to Smoluchowski's coagulation equation for rate kernels that have homogeneity zero but are possibly singular such as Smoluchowski's original kernel. We prove pointwise exponential decay of…

Results from a partial-wave analysis of the reaction $\gamma p \rightarrow K^+ \Lambda$ are presented. The reaction is dominated by the $S_{11}(1650)$ and $P_{13}(1720)$ resonances at low energies and by $P_{13}(1900)$ at higher energies.…