Local existence, global existence and nonexistence of classical solutions for a degenerate and strongly coupled quasilinear parabolic system were studied.
研究一类强耦合拟线性退化抛物方程组初边值问题正古典解的局部存在、全局存在与非全局存在性。
In this paper, the local estimates for the classical solutions of a class of equations and systems in divergence form is obtained by certain kind of function.
文中利用某类函数，得到了一类非线性散度型方程及方程组古典解的局部估计。
In particular, for the case of small initial data with compact support, the author gives the life-span of classical solutions and its application to nonlinear wave equations.
特别地，对紧支集小初值的情况，给出了经典解的生命区间及其在非线性波动方程中的应用。
The present paper provides a class of quasilinear pseudohyperbolic equation of the existence of classical solutions of the first boundary value problem under some suitable structure conditions.
在一定条件下，证明一类拟线性伪双曲方程的第一初边值问题古典解的存在性。
With pairing problems in classical probability as the example and through the forms of several solutions to one problem, the calculating formulas for basic events are presented.
文章以古典概型中“配对”问题的概率为例，采用一题多解的形式，给出了基本事件数的计算公式。
The numerical examples have been presented and compared with the corresponding solutions of classical thin plate theory.
文中给出了算例，并与经典薄板理论的相应解作了对比。
Further, through the exact solutions of the classical equation, the classical phase is derived and the general relation between the quantum phases and the classical phases is also achieved.
进一步通过广义振子经典运动方程的精确解，得出了广义振子的经典相位，从而也得到了广义振子量子相位和经典相位的一般关系。
The method of regularization and the technique of upper and lower solutions are employed to show the local existence and the continuation of the positive classical solution of the above problem.
运用正则化方法和上下解技巧证明了上述问题的古典正解的局部存在性及其可延拓性。
It shows further that solution of the special paradox in classical elasticity is just Jordan canonical form solutions in symplectic space under Hamiltonian system.
结果再次表明经典力学中的弹性楔佯谬解对应的是哈密顿体系下辛几何的约当型解。
But the uniqueness of the weak solutions and the global existence of the classical solution are not obtained.
另外，本部分还研究了相应问题古典解的爆破准则。关于弱解的唯一性和古典解的整体存在性尚未得到证明。
The stationary pulse solutions for a free electron laser are obtained by using the classical theory.
本文用自由电子激光器经典理论的数值解法，给出一组稳定脉冲解。
One advantage of multi-objective genetic optimization algorithms over classical approaches is that many non-dominated solutions can be simultaneously obtained by their single run.
多目标遗传优化算法的一个优点就是可在一次迭代计算中寻找到问题的多个非劣最优解。
After calculating, it shows that this method can effectively improve the calculating precision on the basis of solutions of the classical theories and meet the engineering requirements.
计算表明，该方法能够在经典理论解的基础上有效地提高计算精度，可以满足工程要求。
The classical elementary waves in Riemann solutions include rarefaction wave, shock wave and contact discontinuity.
黎曼解涉及的经典基本波包括疏散波、激波和接触间断。
Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory.
量信息论在物理学，数学和信息科学的国境，正在提供多种解决办法时，是不可能的使用的经典理论。
Second, solve electromagnetic wave propagation of two-dimension concave objects by symplectic Geometrical Theory, and get better field solutions in caustic field2)comparing with classical GO method.
二利用辛几何理论求解电磁波在二维凹面体散射中的传播问题，与经典的GO解比较，特别在焦散区得到较理想的场解。
More important is that the solutions to these two problems will provide the necessary background support for analysis of the qualitative differences between the New Poetry and the classical one.
弄清这两个问题是为分析新诗和旧诗传统的异质性提供背景支持。
Compared with the classical Lie method, it adds an invariant surface condition in the formation. Consequently, it makes calculation easy and obtains more group-invariant solutions.
非古典对称方法在经典的李对称方法的基础上添加了初始方程的表面不变条件，从而既简化了计算，又有助于得到更多的对称及群不变解。
Compared with the classical Lie method, it adds an invariant surface condition in the formation. Consequently, it makes calculation easy and obtains more group-invariant solutions.
非古典对称方法在经典的李对称方法的基础上添加了初始方程的表面不变条件，从而既简化了计算，又有助于得到更多的对称及群不变解。
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