Hyperbolic conservation laws with stiff reaction terms of monostable type
نویسندگان
چکیده
منابع مشابه
Hyperbolic Conservation Laws with Stiff Reaction Terms of Monostable Type
In this paper the zero reaction limit of the hyperbolic conservation law with stiff source term of monostable type ∂tu+ ∂xf(u) = 1 u(1− u) is studied. Solutions of Cauchy problems of the above equation with initial value 0 ≤ u0(x) ≤ 1 are proved to converge, as → 0, to piecewise constant functions. The constants are separated by either shocks determined by the Rankine-Hugoniot jump condition, o...
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Hyperbolic systems often have relaxation terms that give them a partially conservative form and that lead to a long-time behavior governed by reduced systems that are parabolic in nature. In this article it is shown by asymptotic analysis and numerical examples that semidiscrete high resolution methods for hyperbolic conservation laws fail to capture this asymptotic behavior unless the small re...
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In this paper we study the zero reaction limit of the hyperbolic conservation law with stii source term @ t u + @ x f(u) = 1 u(1 ? u 2) : For the Cauchy problem to the above equation, we prove that as ! 0, its solution converges to piecewise constant (1) solution, where the two constants are the two stable local equilibrium. The constants are separated by either shocks that travel with speed 1 ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2001
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-01-02761-1