Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Cauchy problem for an extended model of combustion

Yun-guang Lua1

a1 Institute of Mathematical Sciences, Academia Sinica, P.O. Box 71007, Wuhan 430071, People's Republic of China

Synopsis

This paper considers the Cauchy problem for an extended model of combustion (u + qz)t + f(u)x = 0, zt + kg(u)z = 0 with Lp bounded initial data, where g(u) is a piecewise Lipschitz continuous function and its discontinuous points have no finite limit point. The integral representation gives a definition of a weak solution in Lp space. Some existence results are obtained based on a simplified method of compensated compactness in which the weak continuity theorem of 2 * 2 determinants plays a more important role, but the idea of Young measures has been avoided.

(Received October 08 1990)

(Revised May 25 1991)