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- W628614234 abstract "In this chapter we extend the analysis of Chapter 3 by considering initial-boundary value problem [P,m] for m > 1, namely, $$ left. {begin{array}{*{20}c} {u_t = u_{xx} + u^{_m } + (1 - u), x,t > (P1)} {u(x,0) = u_0 (x), x geqslant 0,(P2)} {u_x (0,t) = 0, t > 0, (P3)} {u(x,t) to 0 as x to infty , t geqslant 0, (P4)} end{array} } right}[P, m] $$when the initial data u(x), is analytic, positive and monotone decreasing function in x ≥ 0, with albebraic decay (up to exponential corrections) of degree ( left( { geqslant frac{1} {{m - 1}}} right) ) as x → ∞ where $${{u}_{0}}(x)sim left{ begin{gathered} tfrac{{{{u}_{infty }}}}{{{{x}^{alpha }}}} + EST(x)asx to infty left( {g1} right) hfill {{{tilde{u}}}_{0}} + sumnolimits_{{n = 1}}^{infty } {{{{tilde{u}}}_{n}}{{x}^{n}}asx to {{0}^{ + }}(g2)} hfill end{gathered} right.$$for some ( left( { geqslant frac{1} {{m - 1}}} right) ), where u ∞, ũ 0 > 0 and ũ n are contants, and EST(x) denotes exponentially small terms in x as x → ∞." @default.
- W628614234 created "2016-06-24" @default.
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- W628614234 date "2004-01-01" @default.
- W628614234 modified "2023-09-27" @default.
- W628614234 title "mth-Order (m > 1) Fisher Nonlinearity: Initial Data with Algebraic Decay Rates" @default.
- W628614234 doi "https://doi.org/10.1007/978-0-85729-396-1_4" @default.
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