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Challenges and opportunities in uncertainty quantification for healthcare and biological systems. [PDF]

open access: yesPhilos Trans A Math Phys Eng Sci
Kimpton LM   +3 more
europepmc   +1 more source
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Carleman weight functions for solving ill-posed Cauchy problems for quasilinear PDEs

Inverse Problems, 2015
Summary: This is the first publication in which a numerical method with rigorously guaranteed convergence is presented for some ill-posed Cauchy problems for semilinear PDEs of the second order. The key tool is the use of the Carleman weight functions in a Tikhonov-like functionals.
Michael Klibanov
exaly   +2 more sources

On a Moment Problem on a Curve Connected with Ill-posed Boundary Value Problems for a PDE and Some Other Problems

2009
This paper is devoted to a connection between ill-posed boundary value problems in a bounded domain for a PDE that isn’t proper elliptic and a new moment problem on a curve that is a generalization of well-known trigonometric moment problem. Some connections with another field of mathematics are given in partial cases of the curve and the equation.
openaire   +1 more source

Carleman estimates for the regularization of ill-posed Cauchy problems

Applied Numerical Mathematics, 2015
Michael Klibanov
exaly  

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