global existence and asymptotic expansion of solutions

... Approximation and Asymptotic Expansion of Solutions 139 operator Kirchhoff or the operator Kirchhoff–Carrier, such as existence of local and global solutions, global regular solutions, the asymptotic ... C.A.: Global existence and stability for wave equation of Kirchhoff type with memory condition at the boundary Nonlinear Anal 54, 959–976 (2003) Linear Approximation and Asymptotic Expansion of Solutions ... theorems and Gronwall’s Lemma, one deduce the existence of a unique weak solution of the problem (1.1)–(1.3) In particular, an asymptotic expansion of a weak solution u = u(ε1 , , εp ) of order

Ngày tải lên: 15/12/2017, 14:41

... scales. In particular, (1.1)isstudiedin[6]with T = Z and p ≡ 0, and in [5] in the case when T = Z with variable p. Much of the organization of and moti- vation for this paper arise from [5, 6].Formoreondelaydynamicequations,see,for ... Massachusetts, 2003 [5] L H Erbe, H Xia, and J S Yu, Global stability of a linear nonautonomous delay difference equation, Journal of Difference Equations and Applications 1 (1995), no 2, 151–161 ... be the linear set of all functions given by Ω : =  x : T → R :  x(t) − p(t)x  k(t)  Δ ∈ C rd  t 0 ,∞  T ;R  ; (1.2) solutions of (1.1)willbelongtoΩ. In the aftermath of Hilger’s breakthrough

Ngày tải lên: 22/06/2014, 22:20

... obtained: asymptotical and exponential stability of DAEs which are of index and [6], Floquet theory of periodic DAEs, criteria for the trivial solution of DAEs with small nonlinearities to be asymptotically ... a C-function of im P (t) of (3.11) Thus, C-classes R of (2.1) and RUimP of the invariant subspace im P of the solution space of (3.11) coincide Suppose that xδ (t) is a solution of the perturbed ... holds for all t ≥ t0 ≥ and any solution x( · ) of (2.1) (2.2) The Central Exponent and Asymptotic Stability The set RA,B of all C-functions of (2.1) is called C-class of (2.1) For any function

Ngày tải lên: 06/08/2014, 05:20

... distributions of the number of edges in a random dissection and in a random outerplanar graph, respectively Proof of Theorem 1.4 The limit distribution of the number of edges in a ... expand the generating... the chromatic number of a random outerplanar graph 5.1 Connectedness, components, and isolated vertices We start with the proof of Theorem 1.3 (1) Proof of ... distribution of the number of components of a specific type, an interesting question is the analysis of the number of copies of a fixed outerplanar graph... distribution of the number of

Ngày tải lên: 07/08/2014, 15:23

... kind if and only if L and R are Andr´e permutations of the first kind. Theorem 7. Let π ∈ S n . Then π is an Andr´e permutation of the first kind if and only if it avoids andr ´ e = and . Proof. Note ... I, and set of values of the right-to- left maxima 2 Here the set of inversions means the set of occurrences of the pattern 21, not the positions of the inversions. the electronic journal of combinatorics ... patterns and the expansion of permutation statistics as sums of permutation patterns Pett er Br? ?and? ?en ∗ Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden Anders Claesson

Ngày tải lên: 08/08/2014, 14:23

... 0 if and only if it is the coefficient of (1+ ζ) n , where 1 +ζ is a root of Φ 2 b+1 (x −1) and b = a i for all i = 1, ··· , l, i.e. 2 b does not appear in the 2-adic expansion of k. Proof: Recall ... some of the ci ’s, i = 1, 2r − 1, are zero Because of this, we write the asymptotic expansion of S(σn,k1 + · · · + σn,ks ) as in (5.32) and decide not to continue with a refinement of ... journal of combinatorics 18(2) (2011), #P8 2 When the asymptotic value of C(F) is zero, we compute the asymptotic values of 1 |λ| n  x 1 , ,x n ∈{0,1} (−1) F (x 1 , ,x n ) , (1.3) where λ and ¯

Ngày tải lên: 08/08/2014, 14:23

... ON ENERGY AND THE ENVIRONMENT: TECHNOLOGY, SCIENCE, AND SOCIETY # 1 Lecture #1 Series Editor: Frank Kreith, professor emeritus, University of Colorado Global Warming and the Future of the Earth ... understandable to the layman, the evidence for and against the idea that global warming due to the emission of CO 2 and other greenhouse gases into the atmosphere is a threat to the future of ... the open ocean both north and south of the equator Because of the rotation of the Earth, water piles up on the western sides of the oceans and flows toward the equator

Ngày tải lên: 04/10/2014, 23:04

... GLOBAL IMBALANCES AND THE COLLAPSE OF GLOBALISED FINANCE GLOBAL IMBALANCES AND THE COLLAPSE OF GLOBALISED FINANCE ANTON BRENDER ... them and to carry the risks involved, in the hope of course of making a profit This form of securitisation... realistic idea of the importance of these funds in the taking of ... – Global Imbalances: Is the world economy really at risk? and Globalised Finance and its Collapse – published by Dexia respectively in May 2007 and April 2009. I ii | GLOBAL IMBALANCES AND

Ngày tải lên: 05/11/2014, 12:36

... example shows that if ker E ⊄ ker F ( n ) then the asymptotic behavior of solutions of the perturbed SDEs (3.1) and the asymptotic behavior of solutions of the unperturbed one may be quite different, ... one, and those of modulus one are semisimple Let Assumptions 1, 2, and hold Then, all solutions of (3.1) are bounded on » (n ) Proof The properties of matrix pencil {E , A} imply that all solutions ... time-varying and arises in the leading term, too Therefore, in this paper we deals with the preservation of asymptotic behavior of the solutions of IDEs when the perturbation is varying in time and affects

Ngày tải lên: 15/12/2017, 05:35

... analysis and asymptotic behavior of solutions to the abstract Cauchy problem, Semigroup Forum 54 (1997), 58–74 B Basit and H Günzler, Asymptotic behavior of solutions of systems of neutral and convolution ... (to the best of our knowledge) except for periodic solutions no necessary and sufficient conditions in terms of the imaginary solutions of characteristic equations and the spectrum of the forcing ... PERIODIC SOLUTIONS OF EQ (1) 3.1 Spectrum of a Mild Solution of Eq (1) We recall that Eq (1) is assumed to be of finite delay and A is assumed to be the generator of a strongly continuous semigroup of

Ngày tải lên: 16/12/2017, 12:27

... America’s Global Involvement and the Emergence of the Cold War   LEARNING OBJECTIVES Identify the economic, political, and ideological factors contributing to the abandonment of isolationism and ... abandonment of isolationism and adoption of globalism post-World War II Understand the definition and origins of the “Cold War consensus.” Define the Yalta and Riga Axioms and identify their significance ... the various components of the policy of “containment” and evaluate its level of effectiveness Identify Roosevelt and Truman’s foreign policy doctrines and evaluate the global context in which

Ngày tải lên: 08/11/2019, 15:01

... America’s Global Involvement and the Emergence of the Cold War   LEARNING OBJECTIVES Identify the economic, political, and ideological factors contributing to the abandonment of isolationism and ... abandonment of isolationism and adoption of globalism post-World War II Understand the definition and origins of the “Cold War consensus.” Define the Yalta and Riga Axioms and identify their significance ... the various components of the policy of “containment” and evaluate its level of effectiveness Identify Roosevelt and Truman’s foreign policy doctrines and evaluate the global context in which

Ngày tải lên: 31/01/2020, 14:30

... scope and improve the understanding of the extent of land cover change in Northern Eurasia and the impact of land-cover distribution and change on a range of ecosystem processes In terms of future ... available for land-cover change detection, validation of land cover and land-cover change products, and development of interdisciplinary research that builds on improved monitoring of land cover  ... exchange and formation of the community of users Further development of NERIN will require maintaining and expanding the ongoing network projects (fire monitoring and NELDA) and development of new

Ngày tải lên: 20/10/2022, 01:48

... damping and source terms,” Journal of Mathematical Analysis and Applications, vol 239, no 2, pp 213–226, 1999 13 Y Zhijian, Existence and asymptotic behaviour of solutions for a class of quasi-linear ... By mean of the Galerkin method and compactness criteria and a difference inequality introduced by Nakao 18 , the author 19, 20 has proved the existence and decay estimate of global solutions ... existence of the solution, that is, T ∞ Thus, the solution u t is a global solution of the problem 1.1 – 1.3 The following theorem shows the asymptotic behavior of global solutions of problem...

Ngày tải lên: 21/06/2014, 18:20

... Next, by the standard continuous arguments, we can obtain the global existence of smooth solutions That is, we combine the local existence and a priori estimate For the local existence of the solution ... together with local existence, leads to global existence of the smooth solutions for IBVP (1.2)–(1.4) by standard continuity arguments In order to obtain the asymptotic behavior and optimal decay ... about the global existence and large time behavior to (1.2) with boundary effect can be found In this article we will consider global existence and asymptotic behavior of smooth solutions to the...

Ngày tải lên: 21/06/2014, 20:20

... applications of differential inclusions On the other hand, it is interesting to mention the existence and nonexistence of global solutions for nonlinear wave equations with nonlinear damping and source ... Liu and M Wang, Global existence and blow-up of solutions for some hyperbolic systems with damping and source terms,” Nonlinear Analysis, vol 64, no 1, pp 69–91, 2006 [5] S A Messaoudi, Global ... the existence of global weak solutions to problem (1.1) is proved by using the potential-well method and the Faedo-Galerkin method In Section 4, the asymptotic stability of the solutions is investigated...

Ngày tải lên: 22/06/2014, 18:20

... applications of differential inclusions On the other hand, it is interesting to mention the existence and nonexistence of global solutions for nonlinear wave equations with nonlinear damping and source ... Liu and M Wang, Global existence and blow-up of solutions for some hyperbolic systems with damping and source terms,” Nonlinear Analysis, vol 64, no 1, pp 69–91, 2006 [5] S A Messaoudi, Global ... the existence of global weak solutions to problem (1.1) is proved by using the potential-well method and the Faedo-Galerkin method In Section 4, the asymptotic stability of the solutions is investigated...

Ngày tải lên: 22/06/2014, 22:20

... assumed solutions The proof of asymptotic behavior of solution is given in Section Journal of Inequalities and Applications Assumptions and Main Results We first give some notations and definitions ... Lp and W0 for Lp Ω and W0 Ω and relevant norms by · p and · 1,p , respectively In general, · X denotes the norm of Banach space X We also denote by ·, · and ·, · the inner product of L2 Ω and ... completes the proof of existence of solution u t To prove the uniqueness, we assume that u t and v t are two solutions which satisfy vt Setting U t ut t , V t vt t , and W t 2.5 - 2.6 and u v , ut...

Ngày tải lên: 21/06/2014, 07:20

... part of Lemma 2.6 only However, this is crucial in the proof of the uniqueness of strong solutions Global existence of strong solutions In this section, we prove the global existence of strong solutions ... important role in the proof of uniqueness of strong solutions Similar conditions were proposed in 16–18 when the authors studied the global existence and uniqueness of solutions of the Navier-Stokes ... can show the global existence of weak solutions without uniqueness if the compatibility conditions 1.9 , 1.10 are not valid We will prove the global existence and uniqueness of strong solutions...

Ngày tải lên: 22/06/2014, 06:20

... part of Lemma 2.6 only However, this is crucial in the proof of the uniqueness of strong solutions Global existence of strong solutions In this section, we prove the global existence of strong solutions ... important role in the proof of uniqueness of strong solutions Similar conditions were proposed in 16–18 when the authors studied the global existence and uniqueness of solutions of the Navier-Stokes ... can show the global existence of weak solutions without uniqueness if the compatibility conditions 1.9 , 1.10 are not valid We will prove the global existence and uniqueness of strong solutions...

Ngày tải lên: 22/06/2014, 19:20