estimate vt. 1.估計,估算;估價;估量。 2.評價,評斷。 3.〔古語〕尊重。 an estimated sum 估計總數。 estimate the loss at 1,000 yuan 估計損失為一千元。 vi. 估計,估價。 n. 1.估計;預測;〔英國〕 〔pl.〕預算,預算額;預算書;估價單;(從典型統計得出的)數值。 2.評價,判斷。 an intelligence estimate 情報[敵情]判斷。 a rough estimate 據粗略的估計。 at a moderate estimate 照適中的估計。 by estimate 照估計。 form an estimate of 給…作一估計;評價。 the E- 〔英國〕財政收支概算。 adj. -d
We solve these difficulties by using the complicated , meticulous a priori estimates 因此,針對不同問題,我們采用一系列復雜的、細致的先驗估計,解決了以上困難。
A priori estimates of incremental unknowns methods on a class of special nonuniform meshes for three dimensional problems 一類特殊非一致網格上三維問題增量未知元方法的先驗估計
Then we apply energy method to get a priori estimate which yields the the global existence and asymptotic result with the help of the local existence result 然后利用能量方法做一個有用的先驗估計,由此估計和局部存在性結果即可得到光滑解的整體存在性和漸近性結果。
In this paper , the main difficulties are from a priori estimates for studing the high dimension , nonlinear systems and unboundary domain , we meet many problems which are difficult to be overcomed by using the standed method 本文的主要特點和難點在于作高維問題、非線性方程組問題及其無界區域問題的先驗估計時,都遇到了許多用常規方法難以克服的困難。
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,考慮一類具耗散的廣義kdv方程組的周期初值問題,在第二節中證明了整體光滑解的存在性和唯一性,得到整體吸引子;在第三節中構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。
In this paper , we consider the global smooth solutions and long time be - haviors for some nonlinear evolution equations , such as kdv equation , bbm equation , gbbm equation , kdv - burgers equation , coupled generalized nonlin - ear wave equation . by using a priori estimates , the existence of global smooth solution , the existence of global attractors and its fractal dimensions for this sys - tems are obtained . this paper is organized in six chapters 本文考察了kdv 、 bbm 、 gbbm 、 kdv - burgers 、廣義耦合的非線性波動方程組等非線性發展方程整體光滑解及其漸近行為,利用先驗估計,對一類廣義kdv方程組及耦合的波動方程組的周期初值問題、 cauchy問題、初邊值問題進行了討論,研究了整體吸引子的存在性及其分形維數有限性估計。
In section 2 . 2 , by a priori estimates and fourier spectral method , we prove the existence and uniqueness of the global smooth solution for the periodic initial value problem and obtain the large time error estimate between spectral approximate solution and the exact solution . in sections 2 . 3 and 2 . 4 , by a priori estimates and galerkin method , we prove the existence of the global smooth solution and global attrac - tors for the initial - boundary value problem . chapter 3 , consider the initial - boundary value problem of the multidimen - sional non - homogeneous gbbm equations 第二章,考慮一類一維非齊次bbm方程,在第二節中利用fourier譜方法和先驗估計證明了具有周期初值問題的整體光滑解的存在性和唯一性,給出了fourier譜近似解和精確解的長時間誤差估計;在第三、四節中討論了初邊值問題,利用與時間t無關的一致先驗估計,證明了整體光滑解和整體吸引子的存在性。
The second section : under the conditions of nonlinear boundary controbility , we consider the initial boundary value problem of camassa - holm equations with dissipative . by using the contractive mapping fixed point theorem and a priori estimates , the existence of global smooth s olution , global attractor in h ~ ( 2 ) , t ime p eriodic s olution or almost - periodic solution and the global exponential stability are proved 第二部分:在非線性控制邊界條件之下,對于帶耗散項的camassa ? holm方程的初邊值問題,用壓縮映射不動點原理及先驗估計方法,證明了整體光滑解的存在性、整體解的指數穩定性、 h ~ 2空間中整體吸引子的存在性以及時間周期解和殆時間周期解的存在性。
This paper uses compare principle to show that there exists at most one of classical solution for ( 1 ) , while the existance of solution is obtained through continuous method . to get the required a priori estimates except the double normal derivatives , we adopt the method in [ 3 ] , and the double normal derivatives on dq are achieved by barrier constructions and applying skill of [ 2 ] 本文用比較原理證明了問題( 1 )至多存在一個古典解,應用連續性方法,得到了問題( 1 )古典解的存在。在得到所需的先驗估計時,利用了[ 3 ]中的方法建立了除去邊界二階法向導數外的先驗估計,通過構造閘函數,用[ 2 ]中的技巧得到在邊界(
百科解釋
In the theory of partial differential equations, an a priori estimate (also called an apriori estimate or a priori bound) is an estimate for the size of a solution or its derivatives of a partial differential equation. A priori is Latin for "from before" and refers to the fact that the estimate for the solution is derived before the solution is known to exist.