Wave propagation under curvature effects in a heterogeneous medium

Chen, X.; Namah, Gawtum

doi:10.1080/00036819708840532

Cited by 18 publications

(17 citation statements)

References 9 publications

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“…Next we apply some of the ideas in [8,9] showing that the average of tan ϕ (or any f (ϕ) where f is increasing) on the interval [−n, n] is a monotonic function of p. Thus, for each fixed α, there is a unique p, such that this average is exactly tan α. We denote this solution (with α fixed) by (c n , ϕ n ).…”

Section: Almost Periodic Traveling Wavesmentioning

confidence: 95%

Traveling waves of a curvature flow in almost periodic media

Lou

Chen

2009

Journal of Differential Equations

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In a plane media with almost periodic vertical striations, we study a curvature flow and construct two kinds of traveling waves, one having a straight line like profile and the other having a V shaped profile. For each of the first-kind traveling waves, its profile is the graph of a function whose derivative is almost periodic. For each of the second-kind traveling waves, its profile is like a pulsating cone, whose two tails approach asymptotically the profiles of the firstkind traveling waves. Also we consider a homogenization problem and provide an explicit formula for the homogenized traveling speed.

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Section: Almost Periodic Traveling Wavesmentioning

confidence: 95%

Traveling waves of a curvature flow in almost periodic media

Lou

Chen

2009

Journal of Differential Equations

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“…This question is related to the passage to the limit in (62) as λ ↓ 0. By the result of [6], it is known that some sequence converges towards a viscosity solution of the Hamilton-Jacobi equation −c + A(z) e −E(z) b g 1 + w 2 z = 0 (with c = c 0 (λ = 0)). Unfortunately, the convergence of the whole family is not clear because this solution is not unique (even up to the addition of a constant).…”

Section: R(y T ) = A(y) E − E(y)mentioning

confidence: 99%

“…Let us continue with some general comments on the literature. Models of similar type are considered in [3,6,12,7,10] but with slightly different assumptions. In [3], the striations are vertical and the front's profile is a straight line.…”

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confidence: 99%

On the propagation of a periodic flame front by an Arrhenius kinetic

Alibaud¹,

Namah²

2017

Interfaces Free Bound.

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We consider the propagation of a flame front in a solid medium with a periodic structure. The model is governed by a free boundary system for the pair "temperature-front." The front's normal velocity depends on the temperature via a (degenerate) Arrhenius kinetic. It also depends on the front's mean curvature. We show the existence of travelling wave solutions for the full system and consider their homogenization as the period tends to zero. We analyze the curvature effects on the homogenization and obtain a continuum of limiting waves parametrized by the limiting ratio "curvature coefficient/period." This analysis provides valuable information on the heterogeneous propagation as well.

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“…In [2], which deals with vertical striations (R(x,y) = R(x),1-periodic), it is shown that there exists a unique 'horizontal' line-shaped traveling front (c, φ), φ being 1-periodic and c the speed of the wave in the y direction. The latter traveling front corresponds therefore to the undulated version of the horizontal line in the case of a constant R.…”

Section: Introductionmentioning

confidence: 99%