Geodesic
Probabilistic models of parabolic conservation and balance laws and systems with switching regimes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 5-42

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We construct a probabilistic representation of the Cauchy problem classical solution for systems of semilinear parabolic equations such that their second order terms enter in a diagonal way with different coefficients while lower order term enter in nondiagonal way. Systems of this kind arise as mathematical models of parabolic conservation and balance laws and as mathematical models of dynamical systems with switching regimes. 
@article{ZNSL_2016_454_a0,
     author = {Ya. I. Belopolskaya},
     title = {Probabilistic models of parabolic conservation and balance laws and systems with switching regimes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--42},
     publisher = {mathdoc},
     volume = {454},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a0/}
}
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Ya. I. Belopolskaya. Probabilistic models of parabolic conservation and balance laws and systems with switching regimes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 5-42. http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a0/