Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Derivation of the Hopf-Cole solution to Burgers' equation by stochastic integrals


Author: S. I. Rosencrans
Journal: Proc. Amer. Math. Soc. 32 (1972), 147-149
MSC: Primary 35.65; Secondary 60.00
DOI: https://doi.org/10.1090/S0002-9939-1972-0289953-5
MathSciNet review: 0289953
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper the Hopf-Cole solution to Burgers' equation is derived by use of stochastic integrals. First the equation is written in Hamilton-Jacobi form, and then, following an idea of Freidlin, the solution is differentiated along a Brownian motion.


References [Enhancements On Off] (What's this?)

  • [1] H. P. McKean, Jr., Stochastic integrals, Probability and Math. Statist., no. 5, Academic Press, New York, 1969. MR 40 #947. MR 0247684 (40:947)
  • [2] E. Hopf, The partial differential equation $ {u_t} + u{u_x} = \mu {u_{xx}}$, Comm. Pure Appl. Math. 3 (1950), 201-230. MR 13, 846. MR 0047234 (13:846c)
  • [3] M. I. Freĭdlin, Quasilinear parabolic equations, and measures in a function space, Funkcional. Anal. i Priložen. 1 (1967), no. 3, 74-82. MR 37 #584. MR 0224985 (37:584)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35.65, 60.00

Retrieve articles in all journals with MSC: 35.65, 60.00


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0289953-5
Keywords: Burgers' equation, stochastic integral, Ito's lemma
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society