GENERALIZED SOLUTIONS OF THE CAUCHY PROBLEM FOR SYSTEMS OF NONLINEAR PARABOLIC EQUATIONS AND DIFFUSION PROCESSES
2012 ◽
Vol 12
(01)
◽
pp. 1150001
◽
Keyword(s):
The purpose of this paper is to construct both strong and weak solutions (in certain functional classes) of the Cauchy problem for a class of systems of nonlinear parabolic equations via a unified stochastic approach. To this end we give a stochastic interpretation of such a system, treating it as a version of the backward Kolmogorov equation for a two-component Markov process with coefficients depending on the distribution of its first component. To extend this approach and apply it to the construction of a generalized solution of a system of nonlinear parabolic equations, we use results from Kunita's theory of stochastic flows.
2000 ◽
Vol 31
(6)
◽
pp. 1270-1294
◽
2013 ◽
Vol 121
(1)
◽
pp. 317-351
◽
2009 ◽
Vol 9
(3)
◽
pp. 429-447
◽
2011 ◽
Vol 19
(4)
◽
pp. 485-501
◽
1987 ◽
Vol 128
(2)
◽
pp. 456-469
◽