双曲问题中的两个问题

The main researches of this item are studying the Cauchy problem of.hyperbolic group with discontinuous coefficient, the global existence and.asymptotic property of solutions of hyperbolic equations with weak degeneration and the topological geometry structure of uncompressed liquid. We have written 29 pieces learning papers about this item, and had published 21 pieces. The main.results include three aspects. The first is studying topological structure with steady state about uncompressed liquid geometry and topology. Second, we obtained the best estimate on blow_up time of solutions of parabolic equations with weak degeneration. Third, we found eigen_diagonalization method and effect on smooth property of classical solution when we use linear eigenvector. Some of our results.was quoted by other experts.

本项目拟定采用最近提出的一种广义解新要领研究间断系数的线性双曲组的柯西问题，以及主要应用微局部分析理论研究具退化的弱双曲方程解的整体存在性和渐近性质。两个问题都是双曲问题中颇有理论意义的课题。本项目的成果无疑将是对整个双曲守恒律理论和非线性双曲型方程解的整体存在性及渐近性理论的丰富和补充，并对其进一步发展起到推动作用。