【作者】 杨丽；

【导师】 张凯军；

【作者基本信息】 东北师范大学 ， 运筹学与控制论， 2006， 硕士

【摘要】 本文考虑了一类任意间断始值u₀的双曲与椭圆耦合系统的初值问题。研究了系统的解的适定性,并进一步利用所得的估计深入讨论了两种松弛极限,即双曲-双曲型,双曲-抛物型的松弛极限。研究解的适定性时采用了粘性消失法,通过粘性逼近方程的解的种种好的性质,利用强收敛过渡到系统的初值问题。对松弛极限的讨论利用了现在广泛使用的伸缩技术,双曲型伸缩:（x,t）→（x/ε,t/ε）和抛物型伸缩技术:u^ε（x,t）=1/εU（x/ε,t/（ε²））,q^ε（x,t）=1/（ε²）Q（x/ε,t/（ε²））。更多还原

【Abstract】 In this paper ,we study the initial value problem for a hyperbolic-elliptic coupled system with arbitrary large discontinuous initial data. We study the well-posedness for that model’s solutions,then further study two kinds of relaxation limits by means of obtained estimates in front sections,which are hyperbolic-hyperbolic and hyperbolic-parabolic relaxation limits.When we study the well-posedness of solutions,we use the classical vanishing viscosity as our tools. By viscosity approximations equations solutions good properties and strong convergences we may turn to the models initial valure problem. Diss-cussing relaxation limits,we use the classical scaling hyperbolic-type scaling:(x, t) → parabolic-type scaling:更多还原