dorsal/arxiv
View SchemaThe Speed of Fronts of the Reaction Diffusion Equation
| Authors | R. D. Benguria, M. C. Depassier |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9511003 |
| URL | https://arxiv.org/abs/patt-sol/9511003 |
| DOI | 10.1103/PhysRevLett.77.1171 |
| Journal | Phys. Rev. Lett., 77 (1996) 1171 |
Abstract
We study the speed of propagation of fronts for the scalar reaction-diffusion equation $u_t = u_{xx} + f(u)$\, with $f(0) = f(1) = 0$. We give a new integral variational principle for the speed of the fronts joining the state $u=1$ to $u=0$. No assumptions are made on the reaction term $f(u)$ other than those needed to guarantee the existence of the front. Therefore our results apply to the classical case $f > 0$ in $(0,1)$, to the bistable case and to cases in which $f$ has more than one internal zero in $(0,1)$.
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"abstract": "We study the speed of propagation of fronts for the scalar reaction-diffusion\nequation $u_t = u_{xx} + f(u)$\\, with $f(0) = f(1) = 0$. We give a new integral\nvariational principle for the speed of the fronts joining the state $u=1$ to\n$u=0$. No assumptions are made on the reaction term $f(u)$ other than those\nneeded to guarantee the existence of the front. Therefore our results apply to\nthe classical case $f \u003e 0$ in $(0,1)$, to the bistable case and to cases in\nwhich $f$ has more than one internal zero in $(0,1)$.",
"arxiv_id": "patt-sol/9511003",
"authors": [
"R. D. Benguria",
"M. C. Depassier"
],
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"doi": "10.1103/PhysRevLett.77.1171",
"journal_ref": "Phys. Rev. Lett., 77 (1996) 1171",
"title": "The Speed of Fronts of the Reaction Diffusion Equation",
"url": "https://arxiv.org/abs/patt-sol/9511003"
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