A. Ramm

activity

19992022

most citedWave scattering by many small particles embedded in a medium

91 citations · 266 across the 35 of their papers we have counts for

collaborators

Showing 2019Show all

5 papers · 1 filter

math.GM2019

Global existence of solutions to nonlinear Volterra integral equations

Alexander G. Ramm

A new method is given for proving the global existence of the solution to nonlinear Volterra integral equations. A bound on the solution is derived. The results are based on a nonl…

math.AP2019

Symmetry problems in harmonic analysis

Alexander G. Ramm

Symmetry problems in harmonic analysis are formulated and solved. One of these problems is equivalent to the refined Schiffer's conjecture which was recently proved by the author.…

math.AP2019

Global existence and uniqueness of the solution to a nonlinear parabolic equation

Alexander G. Ramm

Consider the equation $u^{'} (t) - Δ u + ∣ u ∣^{ρ} u = 0, u (0) = u_{0} (x), (1),$ where $u^{'} := \frac{d u}{d t}$ , $ρ = co n s t > 0,$ $x \in R^{3}$ , $t > 0$ . Assume that $u_{0}$ is a smooth and de…

math.AP2019

Estimating the size of the scatterer

Alexander G. Ramm

Formula for the size of the scatterer is derived explicitly in terms of the scattering amplitude corresponding to this scatterer. By the scatterer either a bounded obstacle $D$ or…

math.GM2019

Theory of hyper-singular integrals and its application to the Navier-Stokes problem

Alexander G. Ramm

In this paper the convolution integrals $\int_{0}^{t} (t - s)^{λ - 1} b (s) d s$ with hyper-singular kernels are considered, where $λ \leq 0$ and $b$ is a smooth or $b$ is in $L^{1} (R_{+})$ .…