得到了激光作用生物组织的热源项，推导了生物热传输方程，并对其定解条件进行了探讨。
We obtained the laser heat source term expression and deduced the bio-tissue heat transfer equation, the solution conditions related were also summarized.
本文研究了半线性波动方程在非线性项和初值满足一定条件下解的存在性。
This paper studies the existence of solution for a semilinear wave equation under the nonlinear term and initial value satisfying certain conditions.
在一定的条件下我们证明了非线性互补问题的解是该微分方程系统的平衡点，并且证明了该微分方程系统的稳定性和全局收敛性。
We prove that the solution of a nonlinear complementarity problem is exactly the equilibrium point of differential equation system, and prove the asymptotical stability and global convergence.
研究一类强退化拟线性抛物方程的重整化解，在一定假设条件下得到了这类广义解的存在惟一性。
The existence and uniqueness of renormalized solutions of a class of strongly degenerate quasilinear parabolic equations under certain assumptions are discussed.
在一定的条件下，得到了上述方程解的增长级与零点收敛指数的精确估计。
Under some conditions, we obtain the precise estimates of the orders of growth and of the exponents of convergence of the zero - sequence of the solutions of the above equations.
从描述电子束运动的基本方程出发，引入一定条件下的近似，获得了一种实用的同轴二极管电流、电压与几何参数关系的近似解析解。
According to the Maxwell equations, an analytic solution related with coaxial diode current, applied voltage and geometry parameters is obtained by introducing certain approximation.
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。
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.
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.
本文用混合隐式特征线法求解了井内流道中的瞬态波动压力问题，给出了弹性管和可压缩流体在井内各流道组合的压力波波动方程和定解条件。
By using the combined implicit characteristic line method, the calculation of the transient surge pressure in the flow conduit of a drilling well has been resolved in this paper.
本文运用正则化方法证明了一类退化抛物方程解的存在唯一性，讨论了解的全局存在性与爆破，并在一定的初值条件下得到了解的爆破速率。
In this paper, we establish the local existence and uniqueness of the solution by using regularization method. We also obtain the global existence and nonexistence. Finally, we get the blow-up rate.
本注记在一定条件下证明了倒向随机微分方程(简记为BSDE)的解满足时齐性，并给出其在金融市场中的解释。
In this note, we give the detail proofs of time-homogeneity of the solution of backward stochastic differential equation (BSDE in short) and their explanations in financial market.
本注记在一定条件下证明了倒向随机微分方程(简记为BSDE)的解满足时齐性，并给出其在金融市场中的解释。
In this note, we give the detail proofs of time-homogeneity of the solution of backward stochastic differential equation (BSDE in short) and their explanations in financial market.
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