8,913 research outputs found
Existence of solutions for the Keller-Segel model of chemotaxis with measures as initial data
A simple proof of the existence of solutions for the two-dimensional
Keller-Segel model with measures with all the atoms less than as the
initial data is given. This result has been obtained by Senba--Suzuki and
Bedrossian--Masmoudi using different arguments. Moreover, we show a uniform
bound for the existence time of solutions as well as an optimal
hypercontractivity estimate
An application of the finite element technique to boundary value problems of potential flow
This report summarizes an experimental application of the finite element approach to two-dimensional inviscid fluid flow. The method results in a matrix equation relating the vector of velocities at the nodal points with the vector of singularities. The singularities, which are concentrated at the nodes, consist of a source and a vortex. On solution of this equation (defining the flow in the region), boundary conditions must te stipulated. This usually involves setting the internal singularities to zero and making certain modifications ro those lying on the boundary of the region. Some results of the application to a particular problem are included in the paper.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50089/1/1620020209_ftp.pd
Precise tail asymptotics of fixed points of the smoothing transform with general weights
We consider solutions of the stochastic equation ,
where is a fixed constant, are independent, identically distributed
random variables and are independent copies of , which are independent
both from 's and . The hypotheses ensuring existence of solutions are
well known. Moreover under a number of assumptions the main being
and , the
limit exists. In the present
paper, we prove positivity of .Comment: Published at http://dx.doi.org/10.3150/13-BEJ576 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
- …