| 1. | An integral formula for bounded domain with piecewise smooth boundary in cn
空间中具有逐块光滑边界的有界域上光滑函数的积分表示 |
| 2. | It can be used in the situations of both smooth boundary and discontinuous boundary . 3
它可以适用于边界光滑或有突变的任何形状槽的分析。 |
| 3. | In this paper , we study classical solution to the first initial - boundary value problem of parabolic hessian equation : where is a bounded , uniformly ( k - l ) - convex domain in rn with smooth boundary
本文研究如下的抛物型hessian方程的第一初边值问题的古典解：其中是r ~ n中有界一致( k - 1 )凸的光滑区域。 |
| 4. | In chapter 4 , we discuss the asymptotic behavior of the weak solution for the initial boundary value problem of the following love equation where fi is a bounded region in rn with smooth boundary
在第四章中，我们借用位势井的思想讨论非线性发展方程的初边值问题整体弱解的渐近性，其中( ? ) r ~ n并具有充分光滑边界， 0 |
| 5. | The limits of stresses in the two categories of elastic bodies with piecewise smooth boundaries and the conditions posed by saint - venant ' s principle are deduced and considered as the mathematical expressions of saint - venant ' s principle for the problems
摘要导出两类具有分片光滑边界面和圣维南原理条件的弹性体中应力分量的极限，并把其作为该两类问题的圣维南原理的数学表达。 |
| 6. | There are three parts in this thesis : chapter 2 consider the initial - boundary value problem where q is a bounded demain in rn with smooth boundary < 3q ; with we show the local existence , the golbal existence and the decay rate of the solutions of that kirchhoff equation
第二章我们考虑了定义在具有光滑边界的有界区域上的kirchhoff型方程初边值问题其中0 ， r ， p 1 ， q 1 ， 1 。这章给出了上述方程解的局部存在性、整体存在性和衰减估计。 |
| 7. | In chapter 3 , 1 consider the nonlinear parabolic equation : where a bounded domain with smooth boundary in ; v is outward normal vector on is a positive function satisfying some compatibility conditions focus my attention on the case of m > 1 , to obtain the blow - up conditions of the positive solution using the method of subsolution and supersolution
运用紧致性原理及moser迭代得到了解的整体存在性和解的熄灭性质。第三章讨论了如下形式的非线性抛物方程：其中m ， ， 0 ， r ~ + ，为r ~ n ( n 1 )中的有界域，具有适当光滑的边界( ? ) ； v是( |
| 8. | Chapter 3 consider the initial - boundary value problem utt - where q is a bounded demain in rn with smooth boundary 3q ; with m ( s ) is a nonnegative c1 - function for s > 0 satisfying with we show that under certain conditions the solution blow up in finite time . chapter 4 consider the initial - boundary value problem and < ? > 2 . we show the decay rate of the solutions of the equation
第三章我们考虑了定义在具有光滑边界的有界区域上的kirchhoff型方程初边值问题其中0 ， r ， p 1 ， q 1 ， 1 ；当s 0时， m ( s )是空间c ~ 1中的非负函数，且满足其中， 0 ， 2这章我们给出了上述方程解的有限时刻爆破条件。 |
| 9. | Then i consider a correlative problem : where m , > 0 , s is a bounded domain with smooth boundary in ; v is outward normal vector on ; f ( s ) is continuous function and satisfies some increasing conditions ; u0 ( x ) is a positive function satisfying some compatibility conditions , to obtain the blow - up conditions of the positive solution using the method of subsolution and supersolution , extend the result of song and zheng
)上的单位外法向； u _ 0 ( x )是正的函数且满足一定的相容性条件：讨论m 1的情况时，在何种条件下使得问题的正解整体存在或是在有限时刻爆破。主要采用上下解的方法来得到结论。随后考虑相关问题：其中m ， 0 ，为r ~ n ( n 1 )中的有界域，具有适当光滑的边界( |
