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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 120, Issue 3-4
  • January 1992, pp. 349-360

Cauchy problem for an extended model of combustion

  • Yun-guang Lu (a1)
  • DOI:
  • Published online: 14 November 2011

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.

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1A. Majda . A qualitative model for dynamic combustion. SIAM J. Appl. Math. 41 (1981), 7093.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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