Probabilistic Representations and Numerical Algorithms for Classical and Viscosity Solutions of the Cauchy Problem for Quasilinear Parabolic Systems
We propose two approaches which allow us to construct probabilistic representations of classical and viscosity solutions of the Cauchy problem for a system of quasilinear parabolic equations. Based on these representations, we develop two numerical algorithms to construct the required solution. The...
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Published in | Journal of mathematical sciences (New York, N.Y.) Vol. 225; no. 5; pp. 733 - 750 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
04.09.2017
Springer Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | We propose two approaches which allow us to construct probabilistic representations of classical and viscosity solutions of the Cauchy problem for a system of quasilinear parabolic equations. Based on these representations, we develop two numerical algorithms to construct the required solution. The system under consideration arises as a mathematical model of parabolic conservation laws. Bibliography: 14 titles. |
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ISSN: | 1072-3374 1573-8795 |
DOI: | 10.1007/s10958-017-3490-5 |