Derivation of the Hopf-Cole solution to Burgers’ equation by stochastic integrals
HTML articles powered by AMS MathViewer
- by S. I. Rosencrans
- Proc. Amer. Math. Soc. 32 (1972), 147-149
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289953-5
- PDF | Request permission
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
- H. P. McKean Jr., Stochastic integrals, Probability and Mathematical Statistics, No. 5, Academic Press, New York-London, 1969. MR 0247684
- Eberhard Hopf, The partial differential equation $u_t+uu_x=\mu u_{xx}$, Comm. Pure Appl. Math. 3 (1950), 201–230. MR 47234, DOI 10.1002/cpa.3160030302
- M. I. Freĭdlin, Quasilinear parabolic equations, and measures on a function space, Funkcional. Anal. i Priložen. 1 (1967), no. 3, 74–82 (Russian). MR 0224985
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- 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