Zero reaction limit for hyperbolic conservation laws with source terms

[摘要] In this paper we study the zero reaction limit of the hyperbolic conservation law with stiff source term partial derivative (t)u + partial derivative (x)f(u) = 1/epsilonu(1-u(2)). For the Cauchy problem to the above equation, we prove that as epsilon --> 0, its solution converges to piecewise constant (+/-1) solution, where the two constants are the two stable local equilibria. The constants are separated by either shocks that travel with speed 1/2(f(1) - f(-1)), as determined by the Rankine-Hugoniot jump condition, or a non-shock discontinuity that moves with speed f'(0), where 0 is the unstable equilibrium Our analytic tool is the method of generalized characteristics. Similar results for more general source term 1/epsilong(u), having finitely many simple zeros and satisfying ug(u) < 0 for large \u\, are also given. (C) 2000 Academic Press.

[发布日期] 2000-12-10