【作者】 刘军；

【导师】 刘红霞；

【作者基本信息】 暨南大学 ， 基础数学， 2002， 硕士

【摘要】 本文研究具有松弛源项的2×2非线性双曲守恒组和2×2非线性粘弹性方程组的初边值问题解的大时间性态。 对此松弛模型，用L~2—能量方法证明了在小扰动的情形下，相应的一般初边值问题的解渐近收敛到一个稳定波或一个稀疏波或这两种非线性波的叠加。 对粘弹性模型，用权能量方法证明了在非凸非退化的情形下，当边界速度为0，初始值具有小扰动时，具初边值问题的解收敛于相应的柯西问题的行波解。更多还原

【Abstract】 The large time behaviors are studied to the initial-boundary problems of 2x2 nonlinear hyperbolic system of conservation laws with relaxation and 2x2 nonlinear system of viscoelasticity in this thesis.Using an L2 energy method proves that the solutions of the general initial-boundary problem to this relaxation model converges time-asymptotically to a stationary wave or a rarefaction wave or superposition of these two kinds wave for small perturbation.Under the assumptions of non-convexity and non-degeneration, it is proved that the solutions of the initial-boundary problem to this viscoelastic model tend towards the travelling wave solution of the corresponding Cauchy problem time-asymptotically for zero boundary speed and small initial perturbation by a weighted energy method.更多还原