Self-similar asymptotics for linear and nonlinear diffusion equations
Publication
, Journal Article
Witelski, TP; Bernoff, AJ
Published in: Studies in Applied Mathematics
January 1, 1998
The long-time asymptotic solutions of initial value problems for the heat equation and the nonlinear porous medium equation are self-similar spreading solutions. The symmetries of the governing equations yield three-parameter families of these solutions given in terms of their mass, center of mass, and variance. Unlike the mass and center of mass, the variance, or "time-shift," of a solution is not a conserved quantity for the nonlinear problem. We derive an optimal linear estimate of the long-time variance. Newman's Lyapunov functional is used to produce a maximum entropy time-shift estimate. Results are applied to nonlinear merging and time-dependent, inhomogeneously forced diffusion problems.
Duke Scholars
Published In
Studies in Applied Mathematics
DOI
ISSN
0022-2526
Publication Date
January 1, 1998
Volume
100
Issue
2
Start / End Page
153 / 193
Related Subject Headings
- Mathematical Physics
- 4901 Applied mathematics
- 0102 Applied Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Witelski, T. P., & Bernoff, A. J. (1998). Self-similar asymptotics for linear and nonlinear diffusion equations. Studies in Applied Mathematics, 100(2), 153–193. https://doi.org/10.1111/1467-9590.00074
Witelski, T. P., and A. J. Bernoff. “Self-similar asymptotics for linear and nonlinear diffusion equations.” Studies in Applied Mathematics 100, no. 2 (January 1, 1998): 153–93. https://doi.org/10.1111/1467-9590.00074.
Witelski TP, Bernoff AJ. Self-similar asymptotics for linear and nonlinear diffusion equations. Studies in Applied Mathematics. 1998 Jan 1;100(2):153–93.
Witelski, T. P., and A. J. Bernoff. “Self-similar asymptotics for linear and nonlinear diffusion equations.” Studies in Applied Mathematics, vol. 100, no. 2, Jan. 1998, pp. 153–93. Scopus, doi:10.1111/1467-9590.00074.
Witelski TP, Bernoff AJ. Self-similar asymptotics for linear and nonlinear diffusion equations. Studies in Applied Mathematics. 1998 Jan 1;100(2):153–193.
Published In
Studies in Applied Mathematics
DOI
ISSN
0022-2526
Publication Date
January 1, 1998
Volume
100
Issue
2
Start / End Page
153 / 193
Related Subject Headings
- Mathematical Physics
- 4901 Applied mathematics
- 0102 Applied Mathematics