Journal article
Solutions to the Nonlinear Recombination Equation for the Infinite Spatial Domain
SIAM journal on applied mathematics, v 29(1)
01 Jul 1975
Abstract
It is shown that the total particle number$N(t) \equiv \int n(\mathbf{x}, t) d^3 x$is bounded below by a certain positive constant for any solution to the recombination equation ∂ n/∂ t = D∇2n- kn2in the infinite (unbounded) spatial domain such that the initial value n(x, 0) is continuous and N(0) is finite. Previously obtained generic results are specialized here to yield general forms n+(x, t) and n-(x, t) which bound n(x, t) above and below for generic n0(x). It is demonstrated that an approximate solution to the generic initial value problem of the associated form$\hat n(\mathbf{x}, t) = (1 - \varepsilon)n_+(\mathbf{x}, t) + \varepsilon n_-(\mathbf{x}, t)$is exact to first order in D for ε a certain algebraic function of the grouping ktn0(x). Finally, supplementary upper and lower bounds on the asymptotic total particle number N(∞) are derived.
Metrics
Details
- Title
- Solutions to the Nonlinear Recombination Equation for the Infinite Spatial Domain
- Creators
- Gerald Rosen
- Publication Details
- SIAM journal on applied mathematics, v 29(1)
- Publisher
- Society for Industrial and Applied Mathematics
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Physics; [Retired Faculty]
- Web of Science ID
- WOS:A1975AE33400014
- Scopus ID
- 2-s2.0-0016535019
- Other Identifier
- 991020705451804721