unbounded space 中文意思是什麼
unbounded space
解釋
無界空間-
By introducing weighted space and using the method of priori estimatehe, uniformly compactness are achieved for s ( t ) in weighted space to overcome the noncom - pactness of the classical sobolev embedding in unbounded domain
在加權空間進行先驗估計，獲得解運算元s （ t ）在加權空間緊的有界吸收集，從而在加權空間得到整體吸引子的存在性。 -
In the second chapter, the kdv type equation on unbounded domain is considered. applying with the method of decomposing operator and the theory of constructing some compact operator in weighted space, the existence of exponential attractor is obtained
在第二章中，運用帶權空間構造一類緊運算元和運算元分解的方法，研究了無界區域上的kdv型方程，得到了該方程指數吸引子的存在性 -
We get the estimates of the upper bounds of hausdorff and fractal dimensions for the global attractors. in section 5. 3, the cauchy problem is studied, by using the weighted function space and the interpolating inequality, the existence of the global attractors for the damped generalized coupled nonlinear wave equations in an unbounded domain is proved. in section 5. 4, the time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary conditions is studied, the existence of time periodic soluation of this problem is proved by using the convergence of approximate time periodic solution sequences
第五章，考慮了一類廣義耦合的非線性波動方程組，在第二節中討論了周期初值問題，證明了整體光滑解的存在性和唯一性，得到了整體吸引子，給出了hausdorff維數和分形維數的上界估計；在第三節中討論了cauchy問題，利用加權函數和加權空間的插值不等式，證明了無界區域上整體吸引子的存在性；在第四節中證明了時間周期解的存在性。 -
Chapter 6, consider a coupled generalized kdv - burgers equation. in section 6. 2, we study the initial - boundary value problem in the semi - unbounded domain, the existence of global solutions and global attractors is proved by means of a uniform priori estimate for time. in section 6. 3, the cauchy problem by using the weighted space, the existence of the global attractors for a coupled generalized kdv - burgers in an semi - unbounded domain is proved
第六章，考慮了一類廣義耦合的kdv - burgers方程，在第二節中討論了半無界區域上的初邊值問題，證明了整體光滑解和整體吸引子的存在性；在第三節中討論了cauchy問題，利用加權函數和加權空間上的插值8不等式，證明了半無界區域上整體吸引子的存在性。 -
The paper is concerned with periodic solutions to nonautonomous second order hamilton systems where, m : [ 0, t ] - s ( rn, rn ) is a continuous mapping in the space s ( rn, rn ) of symmetric real ( n x n ) - matrices, such that for some u > 0 and all ( t, z ) [ 0, t ] x rn, ( m ( t ) x, x ) > u | x | 2. a s ( rn, rn ), f : [ 0, t ] x rn r is continuous and f : [ 0, t ] xr r exists, is continuous and we study the existence of periodic solutions of the systems by using ekeland variational principle and the saddle points theorem. we suppose that the nonlinearity vf and potential f belongs to a class of unbounded functional. our work improves the existed results. we obtained the results of multiplicity of periodic solutions of the systems by using lusternik - schnirelman category theory and the generalized saddle points theorem, and the functional does not need the condition of constant definite. at last, we obtained the existence of infinity many distinct periodic solutions of the corresponding non - perturbation systems by using the symmetric mountain pass theorem
（ ? ， ? ）為r ~ n中內積， | ? |為對應范數。 f [ 0 ， t ] r ~ n r連續， ? f （ t ， x ）存在且連續， h l ~ 1 （ 0 ， t ； r ~ n ） 。利用ekeland變分原理和鞍點定理討論了該系統周期解的存在性，把非線性項和位勢函數放寬到一類無界函數，推廣了這方面工作的一些已有結果；利用廣義鞍點定理和lusternik - schnirelman疇數理論得到了該系統的多重周期解，取掉了泛函的常定要求；最後利用對稱山路定理得到沒有擾動時系統的無窮多周期解。 -
The second problem is the comparison principle on the full space. for the viscosity supsolution and subsolution v and u, we have the result u < u on the condition that lim finally, we investigate the compar - iaon principle for unbounded functions on the full space. when the equation ' s subsolution and supsolution u and v satisfy c is constant ) and the proper assumptions of the equation and the measure, we proved the comparison principle
第二個問題是全空間上的比較原理，對這類方程的上下解v和u ，只要，也有比較結果u v ，最後討論全空間上無界函數的比較原理，當方程的上、下解低於一次增長，在對方程和測度的適當假設下，證明了粘性解的比較原理。 -
At the same time, the mechanics mode of newly - built structure is not the same as that single cavern is excavated in the half - unbounded space. its original stress field is disturbed by former time and time again, and once more by excavating of later. so the mechanics mode of the later is not symmetrical generally and infinite variability is put up
同時新建結構物的受力模式也不同於半無限體或無限體中修建單一洞室的一般狀況，其初始應力場往往是經過多次擾動的，其施工將再次進行擾動，使其受力往往是非對稱的，表現出極大的變異性。
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