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Reconstruction of a piecewise smooth absorption coefficient by an acousto-optic process
acousto-optic inverse problem spherical Radon transform Helmholtz decomposition piecewise smooth functions reconstruction Landweber iteration stability
2012/6/27
The aim of this paper is to tackle the nonlinear optical reconstruction problem. Given a set of acousto-optic measurements, we develop a mathematical framework for the reconstruction problem in the ca...
Existence and uniqueness of very singular solutions for a fast diffusion equation with gradient absorption
Very singular solution singular diffusion gradient absorption self-similar solutions p-Laplacian uniqueness
2011/8/26
Abstract: Existence and uniqueness of radially symmetric self-similar very singular solutions are proved for the singular diffusion equation with gradient absorption {equation*} \partial_t u -\Delta_{...
Singular solutions to the heat equations with nonlinear absorption and Hardy potentials
Singular solutions heat equations nonlinear absorption Hardy potentials
2010/12/10
We study the existence and nonexistence of singular solutions to the equation ut−u−
|x|2 u + |x| u|u|p−1 = 0, p > 1, in RN × [0,∞), N ≥ 3, with a singularity at the point
(0, 0)...