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- W90288657 abstract "Abstract This work is concerned with travelling front solutions of semilinear parabolic equations in an infinite cylindrical domain Σ = R × ω where ω ⊂ Rn−1 is a bounded domain. We write for x in Σ, x = (x1, y), with y ∊ ω. The problems we consider are of the following type { Δ u − ( c + α ( y ) ) ∂ 1 u + f ( u ) = 0 in Σ ∂ u ∂ ν = 0 on ∂ ∑ u ( − ∞ , . ) = 0 , u ( + ∞ , . ) = 1 where the unknowns are the parameter c ∊ R and the function u. The function α ∈ C 0 ( ω ¯ ) and the nonlinear term f: [0, 1] → R are given. (More general coefficients than c + α (y), β (y, c) are also treated.) We obtain a fairly general resolution of this problem. The results depend on the type of nonlinearity considered. When f is of the bistable type, or of the “ignition temperature” type in combustion, we show the existence and uniqueness of c and of the profile u. In the case that f > 0 in (0, 1), we show the existence of c* ∊ R such that a solution exists if and only if c ≧ c*. These results extend to higher dimensions various classical results. In particular they extend the result of Kolmogorov, Petrovsky and Piskounov." @default.
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- W90288657 date "1992-10-01" @default.
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- W90288657 title "Travelling fronts in cylinders" @default.
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- W90288657 doi "https://doi.org/10.1016/s0294-1449(16)30229-3" @default.
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