具耗散项拟线性双曲方程组柯西问题整体解的存在性与非存在性

Existence and Nonexistence of Globally Smooth Solutions of Cauchy Problem of Quasilinear Hyperbolic Systems with Dissipative Terms

对于一类具耗散项拟线性双曲型方程组,在始值合理假设下,本文证明了其柯西问题整体光滑解的存在性与非存在性。结果表明,即使加强耗散项而且始值 C°模充分小,其柯西问题的解仍可能在有限时间内发生奇性.

In this paper,for a class of quasilinear hyperbolic systems,author has proved global existence and nonexistence of smooth solutions for its Cauchy problem.This result shows that it is possible to present singularity for solu- tions of its Cauchy problem in finite time,even though the dissipative term is strengthened and the smallness of C°norm of initial data is satisfied.