dorsal/arxiv
View SchemaA Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation
| Authors | R. D. Benguria, M. C. Depassier |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9410001 |
| URL | https://arxiv.org/abs/patt-sol/9410001 |
| DOI | 10.1103/PhysRevE.52.3285 |
| Journal | Phys. Rev. E, 52 (1995) 3285 |
Abstract
We show that the minimal speed for the existence of monotonic fronts of the equation $u_t = (u^m)_{xx} + f(u)$ with $f(0) = f(1) = 0$, $m >1$ and $f>0$ in $(0,1)$ derives from a variational principle. The variational principle allows to calculate, in principle, the exact speed for arbitrary $f$. The case $m=1$ when $f'(0)=0$ is included as an extension of the results.
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"abstract": "We show that the minimal speed for the existence of monotonic fronts of the\nequation $u_t = (u^m)_{xx} + f(u)$ with $f(0) = f(1) = 0$, $m \u003e1$ and $f\u003e0$ in\n$(0,1)$ derives from a variational principle. The variational principle allows\nto calculate, in principle, the exact speed for arbitrary $f$. The case $m=1$\nwhen $f\u0027(0)=0$ is included as an extension of the results.",
"arxiv_id": "patt-sol/9410001",
"authors": [
"R. D. Benguria",
"M. C. Depassier"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.52.3285",
"journal_ref": "Phys. Rev. E, 52 (1995) 3285",
"title": "A Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation",
"url": "https://arxiv.org/abs/patt-sol/9410001"
},
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