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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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 225; no. 5; pp. 733 - 750
Main Authors Belopolskaya, Ya. I., Nemchenko, E. I.
Format Journal Article
LanguageEnglish
Published New York Springer US 04.09.2017
Springer
Springer Nature B.V
Subjects
Algorithms
Cauchy problems
Conservation laws
Environmental law
Laws, regulations and rules
Mathematical models
Mathematics
Mathematics and Statistics
Representations
Viscosity
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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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-017-3490-5