The existence of global smooth so - lution and global attractors of this problem was proved by means of a uniform priori estimate for time . chapter 4 , consider the periodic initial value problem of a dissipative gen - eralized kdv equations 第三章,考慮高維的非齊次gbbm方程的初邊值問(wèn)題,建立與時(shí)間t無(wú)關(guān)的一致先驗(yàn)估計(jì),證明了整體光滑解和整體吸引子的存在性。
Nai - heng chang , j . shatah , k . uhlenbeck considered the initial value problem for the 2 - dimensional cylindrical symmetric case in 1999 , they proved that there exists one global smooth solution under the energy small initial condition 1999年changnaiheng 、 jalalshatak和uhlenbeck考慮了它的2 -維柱對(duì)稱(chēng)情形的初值問(wèn)題,在小初始能量條件下,他們證明了它存在一個(gè)整體光滑解。
Based on the asymptotic properties for numerical integral formulas , this paper obtains a class of finite difference methods for solving initial value problems of odinary differential equations , and studies the consistency and stability of new methods 摘要基于數(shù)值積分公式中間點(diǎn)的漸近性質(zhì),獲得了一類(lèi)求解常微分方程初值問(wèn)題有限差分方法,研究了新方法的相容性和穩(wěn)定性。
By the structure of weak entropy solution of corresponding initial value problem and the boundary entropy condition which was developed by bardos - leroux - nedelec , we give a construction method to the weak entropy solution of the initial - boundary value problem 由相應(yīng)的初始值問(wèn)題弱熵解的結(jié)構(gòu)和bardos - leroux - nedelec提出的邊界熵條件,給出初邊值問(wèn)題弱熵解的一個(gè)構(gòu)造方法。
A formula to solve the initial value problem of homogeneous linear differential equations with constant coefficients is given and a formula to solve the homogeneous linear difference equations with constant coefficients under certain conditions is derived 摘要給出了常系數(shù)齊次線性微分方程組初值問(wèn)題的一個(gè)求解公式,并由此推出常系數(shù)齊次線性差分方程組在給定的初始條件下的一個(gè)求解公式。
In this paper , we use the coupled fixed point theorem for mixed monotone condensing operators to obtain an existence , uniqueness and iterative approximation theorem of solutions of initial value problems for second order mixed monotone type of impulsive differential equations 利用混合單調(diào)凝聚算子的耦合不動(dòng)點(diǎn)定理,給出了二階混合單調(diào)型脈沖微分方程的初值問(wèn)題的解的存在唯一性及迭代逼近定理
Compared with the initial value problem , the weak entropy solution of the initial - boundary value problem includes the following new interaction type : a central rarefaction wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary 與初始值問(wèn)題相比較,初邊值問(wèn)題的弱熵解包含了以下新的相互作用類(lèi)型:中心稀疏波與邊界相撞,邊界反射出一個(gè)與之相切的新激波。
By solving the initial value problem of the positional differential equation of the parallel manipulator , not only the position of platform can be determined when the lengths of six legs were specified , but also the transition positions between the two specified leg lengths can be determined 該方法通過(guò)求解并聯(lián)機(jī)構(gòu)位姿方程的微分初值問(wèn)題,經(jīng)過(guò)路徑跟蹤,可求出指定桿長(zhǎng)動(dòng)平臺(tái)的正確位姿,并可求出從初值到待求值的中間結(jié)果。
4 . by using the theory of cones and the partial - ordered method with upper solution or lower solution . existence and uniqueness of global solutions on interval [ 0 , a ] ( a > 0 ) for the first order initial value problem of discontinuous equations in banach space ( 1 ) is discussed 利用半序方法,只用上解或下解得到了banach空間中含有間斷項(xiàng)的常微分方程初值問(wèn)題( 1 )在[ 0 , a ] ( a 0 )上整體解的兩個(gè)存在唯一性結(jié)果,并給出了解的誤差估計(jì)式。
The convergence and stability for the schemes are proved , and the error estimates are obtained . chapter 5 , consider the damped coupled generalized nonlinear wave equations . in section 5 . 2 , by coupled a priori estimates and galerkin method , prove the existence and uniqueness of the global smooth solution for the periodic initial value problem and obtain the existence of global attractors 第四章,考慮一類(lèi)具耗散的廣義kdv方程組的周期初值問(wèn)題,在第二節(jié)中證明了整體光滑解的存在性和唯一性,得到整體吸引子;在第三節(jié)中構(gòu)造了半離散和全離散的fourier譜格式和擬譜格式,在整體光滑解存在的條件下,證明了這些格式解的收斂性,并得到了誤差估計(jì)。
In mathematics, in the field of differential equations, an initial value problem (also called the Cauchy problem by some authors) is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution. In physics or other sciences, modeling a system frequently amounts to solving an initial value problem; in this context, the differential equation is an evolution equation specifying how, given initial conditions, the system will evolve with time.