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本文考察了一类拟线性双曲抛物耦合方程组的初边值问题,它包含了辐射流体力学方程组、粘弹性力学方程组等作为其特殊情形。文中应用能量估计方法以及延拓性讨论,证明了小初值条件下的整体光滑解的存在唯一性以及当t→+∞时解的指数衰减性质;并将所得结果应用于辐射流体力学及粘弹性力学方程组的相应的初边值问题。 相似文献
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郑宋穆 《数学年刊B辑(英文版)》1984,(4)
本文考察了具耗散项的一阶拟线性对称双曲组柯西问题的整体光滑解.应用对非线性问题解的一致先验估计以及延拓法,证明了在小初值的条件下整体光滑解的存在唯一性以及当t→ ∞时,解的指数衰减率. 相似文献
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郑宋穆 《数学年刊B辑(英文版)》1983,(4)
The initial bounary value problem for quasilinear hyperbolic-parabolic coupled systemsin higher dimensional spaces,which arises in many mechanical problems is considered.Underthe assumptions that the hyperbolic part of the coupled system is a quasilinear symmetrichyperbolic system and the parabolic part is a quasilinear parabolic system of second orderand suitble asstunptions of smoothness and compatibiliy conditions,the existence anduniqueness of local smooth solution is proved in the cases that the boundary of domain isnoncharacteristic or uniformly characteristic with respect to the hyperbolic part.As an application,the existence and uniqueness of local smooth solution for the initialboundary problem of the radiation hydrodynamic system,as well as of the viscous compressiblehydrodynamic system,with solid wall boundary,is obtained. 相似文献
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郑宋穆 《数学年刊A辑(中文版)》1984,(4)
本文考察了具耗散项的一阶拟线性对称双曲组柯西问题的整体光滑解,应用对非线性问题解的一致先验估计以及延拓法,证明了在小初值的条件下整体光滑解的存在唯一性以及当t→+∞时,解的指数衰减率。 相似文献
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郑宋穆 《数学物理学报(B辑英文版)》1987,(4)
§1. Introduction In this paper we are concerned with the following initial boundary value problem for nonlinear parabolic equations: where Γ is the smooth boundary of a bounded domain Ω∈R~n, x=(x_1,…x_n), D_xu=(u_(x_1),… u_(x_n)), D_x~2=(u_(x_ix_j)), (i, j=1, …,n). What we want do do in this paper is to consider the global existence of smooth solutions for (1.1) under the assumption of small initial data. 相似文献
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郑宋穆 《数学年刊A辑(中文版)》1984,(6)
在适当的耗散条件下,只要初始资料适当小证明了高维拟线性双曲抛物耦合方程组柯西问题的整体光滑解的存在唯一性。 相似文献
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