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Abstract ( Alexandre Boukhgueim )
Attenuated vector tomography on the plane
Using the theory of A-analytic functions we obtain exact inversion formulas
for recovering the full vector field through its scalar attenuated Radon
transform.
Abstract ( Chun Liu )
On Viscoelastic Fluids
In this talk, I will present some recent results on several different models for
the viscoelastic materials.
Abstract ( Chunshan
Zhao )
Locating the peaks of least energy solutions to a class of
quasi-linear elliptic Neumann problems
We study the shape of least energy solutions to a class of singularly
perturbed quasi-linear elliptic equations with Neumann boundary conditions.
First we give an upper bound for the least energy which is closely related to
the mean curvature of boundary. Then we locate the point where concentration
happens.
Some symmetry properties of the least energy solutions will also be presented.
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Abstract ( Victor
Isakov )
Increased stability in the Cauchy problem for the Helmholtz
equation
We consider the Cauchy problem for the Helmholtz equation with the
data on some surface S. We give a new estimate showing that when frequency/wave
number in increasing, the stability of solution u to the Helmholtz equation is
increasing in the convex hull of S. The proof consists of splitting u into
high- and low frequency components and using standard hyperbolic energy
estimates for low frequencies and new Carleman type estimates for high
frequencies. Due to classical results of Fritz John with growing frequency
stability deteriorates outside of convex hull of S. WE formulate open problems
and future direction of research.
Abstract ( Gary
Lieberman)
Some unusual regularity results for singular
parabolic equations
It is well-known that solutions of the heat equation are quite
regular in the parabolic interior of their domain of definition; however, the
same is not true of solutions of p-Laplace type equations with p close to one.
In this talk, we show that the local regularity of the solution is controlled by
its initial regularity.
Abstract ( Lihe
Wang )
Existence and estimates on parabolic Reifenberg flat
domains