Preprint 1998-037

Zero Reaction Limit for Hyperbolic Conservation Laws with Source Terms

Abstract: In this paper we study the zero reaction limit of the hyperbolic conservation law with stiff source term

u_t + f(u)_x = 1/eps u ( 1-u² ).

For the Cauchy problem to the above equation, we prove that as $\eps\to 0$, its solution converges to piecewise constant ($\pm 1$) solution, where the two constants are the two stable local equilibrium. The constants are separated by either shocks that travel with speed $\frac12(f(1)-f(-1))$, as determined by the Rankine-Hugoniot jump condition, or a non-shock discontinuity that moves with speed $f'(0)$, where $0$ being the unstable equilibrium. Our analytic tool is the method of generalized characteristics. Similar results for more general source term ${1\over \eps}g(u)$, having

Paper:

Available as PostScript .

Title:

Zero reaction limit for hyperbolic conservation laws with source terms

Author(s):

Haitao Fan

Shi Jin

Zhen-Huan Teng

Publishing information:

Comments:

Submitted by:

mailto:jin@math.gatech.edu October 21 1998.