文中证明了该问题古典解的局部存在性、整体存在性和唯一性。
The local existence, the global existence and the uniqueness of a classical solution of this problem are proved.
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。
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.
讨论一类退缩拟线性抛物方程组解的局部存在性与猝灭，证明了在一定条件下解在有限时刻发生猝灭，并给出猝灭时间的一个上限估计。
A class degenerate quasilinear parabolic systems is considered. The local existence is proved. In some conditions the solution quench in a finite time. And an estimate of quenching time is given.
因此，可获得局部解的存在性。
然后利用压缩映象原理方法，证明了方程局部广义解的存在唯一性；
Secondly, the existence and uniqueness of the generalized local solution is obtained using the contraction mapping principle.
我们将利用正则化方法和上下解技巧给出局部古典解和整体古典解的存在唯一性。
We will use regularization method and upper and lower solution technique to give the local existence, global existence and uniqueness results.
本文第三章讨论的是如下非局部边界条件的反应扩散系统解的存在性和唯一性。
In the chapter there of this paper, we consider the uniqueness and the existence of solutions of the following reaction diffusion system with nonlocal boundary conditions.
主要运用能量方法及稳定集和不稳定集的观点，研究一类半线性抛物方程的整体解和局部解的存在性及爆破问题。
In this paper, we are concerned with the existence of global solutions or local solutions and blowup of one kind of semilinear heat equation.
在一定条件下给出了这类问题平衡解的局部分支性质，包括分支解的存在性和分支解的个数。
The local bifurcation properties of equilibrium solution of the system follows from our results, including the information of the existence and the Numbers of the bifurcation solutions.
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。
Local existence, global existence and nonexistence of classical solutions for a degenerate and strongly coupled quasilinear parabolic system were studied.
讨论了伪抛物方程的一类非线性非局部边值问题，得到了当区域固定时解的存在唯一性，并就当区域变化时解的极限性态进行了探。
The existence and uniqueness of solution are proved when the domain is fixed, and the limit behaviour of solutions is obtained as the domain is changed.
获得了解的整体存在惟一性，并给出了非平凡平衡解局部渐近稳定性易验证的充分条件。
The global existence-uniqueness of solutions is obtained and the easy verifiable sufficient conditions for local asymptotic stability of a non-trivial steady-state solutions are given.
本文采用局部间断有限元方法，给出其数值通量形式并证明了其数值解的存在唯一性。
In this paper, we introduce the numerical flux of the LDG method (local discontinuous Galerkin method) and prove the existence and uniqueness of the LDG numerical solution.
本文采用局部间断有限元方法，给出其数值通量形式并证明了其数值解的存在唯一性。
In this paper, we introduce the numerical flux of the LDG method (local discontinuous Galerkin method) and prove the existence and uniqueness of the LDG numerical solution.
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