Hindawi Publishing Corporation Boundary Value Problems Volume 2010, Article ID 796065, 21 pages doi:10.1155/2010/796065 Research Article One-Dimensional Compressible Viscous Micropolar Fluid Model: Stabilization of the Solution for the Cauchy Problem Nermina Mujakovi ´ c Department of Mathematics, University of Rijeka, Omladinska 14, 51000 Rijeka, Croatia Correspondence should be addressed to Nermina Mujakovi ´ c, mujakovic@inet.hr Received 8 November 2009; Revised 24 May 2010; Accepted 1 June 2010 Academic Editor: Salim Messaoudi Copyright q 2010 Nermina Mujakovi ´ c. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We consider the Cauchy problem for nonstationary 1D flow of a compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. This problem has a unique generalized solution on R×0,T for each T>0. Supposing that the initial functions are small perturbations of the constants we derive a priori estimates for the solution independent of T, which we use in proving of the stabilization of the solution. 1. Introduction In this paper we consider the Cauchy problem for nonstationary 1D flow of a compressible viscous and heat-conducting micropolar fluid. It is assumed that the fluid is thermody- namically perfect and polytropic. The same model has been considered in 1, 2, where the global-in-time existence and uniqueness for the generalized solution of the problem on R×0,T,T>0, are proved. Using the results from 1, 3 we can also easily conclude that the mass density and temperature are strictly positive. Stabilization of the solution of the Cauchy problem for the classical fluid where microrotation is equal to zero has been considered in 4, 5.In4 was analyzed the H ¨ older continuous solution. In 5 is considered the special case of our problem. We use here some ideas of Kanel’ 4 andtheresultsfrom1, 5 as well. Assuming that the initial functions are small perturbations of the constants, we first derive a priori estimates for the solution independent of T. In the second part of the work we analyze the behavior of the solution as T →∞. In the last part we prove that the solution of our problem converges uniformly on R to a stationary one. 2 Boundary Value Problems The case of nonhomogeneous boundary conditions for velocity and microrotation which is called in gas dynamics “problem on piston” is considered in 6. 2. Statement of the Problem and the Main Result Let ρ, v, ω,andθ denote, respectively, t he mass density, velocity, microrotation velocity, and temperature of the fluid in the Lagrangean description. The problem which we consider has the formulation as follows 1: ∂ρ ∂t ρ 2 ∂v ∂x 0, 2.1 ∂v ∂t ∂ ∂x ρ ∂v ∂x − K ∂ ∂x ρθ , 2.2 ρ ∂ω ∂t A ρ ∂ ∂x ρ ∂ω ∂x − ω , 2.3 ρ ∂θ ∂t −Kρ 2 θ ∂v ∂x ρ 2 ∂v ∂x 2 ρ 2 ∂ω ∂x 2 ω 2 Dρ ∂ ∂x ρ ∂θ ∂x 2.4 in R × R , where K, A,andD are positive constants. Equations 2.1–2.4 are, respectively, local forms of the conservation laws for the mass, momentum, momentum GI I PHÁP CUNG C P ĐI N -AN TOÀN ĐI N TRONG B NH VI N Gi i pháp cung c p n cho b nh vi n v i h u n giám sát HospEC T ng quan Gi i pháp HospEC Ch ng nh n ch t l ng – b nh vi n Gi i pháp h th ng s n ph m c a chúng tôi: S n ph m c a + T phân ph i LV đ c TEST; + Phù h p v i tiêu chu n quy đ nh m i + H th ng u n giám sát ngu n cung c p n nh t c a B nh vi n phù h p v i IEC 60364-7-710:2002VDE 0100-710:2002-11/TCVN7447-7+ c ki m tra ch ng nh n b i phòng 11/DIN 710:2006; thí nghi m, th nghi m đ c l p Chúng ho t đ ng c s m t h th ng + Hi n th Panel u n công ngh hi n đ i qu n lý ch t l ng đ c ch ng nh n theo + H th ng giám sát dòng n; dòng n rò; cách n tiêu chu n DIN/ ISO 9001:2000 h th ng cung c p n IT; nhi t đ ,… V i l i th nhi u n m kinh nghi m th c hi n an D ch v toàn n b nh vi n, c s y t + T v n, thi t k ; + Phân tích, t ng h p m ng cung c p n; + Qu n lý d án k ho ch; +H ng d n đào t o chuy n giao công ngh ; + D ch v Hotline; + D ch v b o trì, s a ch a Page of 22 Gi i pháp cung c p n cho b nh vi n v i h th ng u n giám sát HospEC H th ng cung c p n 2.2 Module giám sát chuy n đ i cho h th ng IT (trung tính cách ly) nhóm 1.1 T phân ph i n t ng 2.3 H th ng phát hi n l i cách ly 1.2 T phân ph i n cho tòa nhà khu v c 2.4 H th ng giám sát dòng n dòng n rò m ng TN/TT 1.3 T phân ph i n IPS cho m ng n IT (trung tính cách ly) cho nhóm 2.5 Màn hình v n hành hi n th 1.4 T phân ph i n SD (TT/TN) cho nhóm 2.6 i u n chi u sáng k t n i v i h th ng khác v i thi t b I/O MPM H th ng u n giám sát HospEC 2.7 Chu n truy n thông CAN bus 2.1 Module chuy n đ i ngu n cho t ph i phân Page of 22 Thi t b u n giám sát HospEC B nh nhân trung tâm c a m t b nh vi n ho c c s y t Vi c cung c p n b gián đo n có th d n đ n tình hu ng nguy hi m vi c u tr gây nguy hi m cho s c kh e c a b nh nhân tr ng h p n ng Nh v y, B nh vi n, c s y t đ c coi h tiêu th n lo i 1, (tiêu th n lo i h tiêu th b m t n, ng ng c p n d n đ n nguy hi m đ n tính m ng ng i, gây thi t h i l n, h h ng máy móc, thi t b , …) v i h tiêu th n ph i đ c c p n t ngu n đ c l p, ph i có ngu n d phòng nóng Thi t k h th ng cung c p n cho b nh vi n m t v n đ c c k quan tr ng, h th ng c p n yêu c u ph i an toàn cao, đ tin c y l n, đ c bi t ph i đ c c p n 24/24h ngày V i đòi h i th c t , H th ng u n giám sát HospEC c a ESA Elektroschaltanlagen Grimma GmbH – c đ c phát tri n phân ph i b i Sigma Vietnam System JSC v i m c đích đ cung c p an toàn n b nh vi n ho c c s y t H th ng c a đáp ng yêu c u cao nh t v an toàn cung c p n t i b nh vi n ho c c s y t tuân theo tiêu chu n IEC 60364-7-710:2002-11 DIN VDE 0100-710:2002-11 Gi i pháp c a HospEC H th ng u n giám sát HospEC đ c tích h p gi i pháp an toàn n h th ng n cung c p b nh vi n tin c y, hi u qu kinh t V i công ngh c a chúng tôi: T i u u ch nh, ki m soát t t c m c n thi t, giám sát ki m soát đáp ng yêu c u h th ng cung c p n c a m t b nh vi n ho c c s y t S linh ho t c a HospEC cho phép ng d ng hi u qu h u h t tình hu ng khác H th ng v i ch c n ng ph c t p c a nó, thi t k cài đ t đ n gi n u m + Giám sát tin c y, l u tr , ki m soát hi n th tình tr ng ho t đ ng c a h th ng phân ph i n theo tiêu chu n IEC 60364-7-710:2002-11 DIN VDE 0100-710:2002-11; + Tích h p h th ng m (cho phép k t n i v i h th ng khác); + Kh n ng k t n i v i thành ph n khác thông qua mô-đun I/O k thu t s ; + D dàng m r ng ho c thích ng c a c u trúc mô-đun; + T i u hóa chi phí; + Thi t k , l p đ t v n hành đ n gi n; + Gi m thi u th i gian: thi t k , l p đ t v n hành; + Tính s n sàng đ tin c y cao b ng cách ki m soát chéo c a thi t b h th ng; + B o trì, b o d ng đ n gi n, chuy n giao công ngh b i chuyên gia c a Page of 22 Gi i pháp t phân ph i n t ng - LVMD T b ng phân ph i n t ng t phân ph i n trung tâm sau tr m bi n áp máy phát n d phòng b nh vi n (c s y t ) Trong bao g m ngu n c p n chung (GS – ngu n t l i n) ngu n c p n d phòng (SS – ngu n t máy phát n d phòng) V i yêu c u quan tr ng nghiêm ng t ngu n cung c p n cho b nh vi n (c s y t ) ph i có đ n đ nh, tin c y cao Do đó, h th ng đ c bi t t phân ph i n t ng LVMD ph i đ c ki m tra, th nghi m ph i tuân theo quy đ nh nghiêm ng t th gi i: tiêu chu n DIN VDE 0660 Part 500, IEC 60439-1 DIN EN 60439-1 Gi i pháp Phân ph i n t ng bao g m: + u vào/ra ngu n c p n theo ngu n n chung (GS); + u vào/ra ngu n c p n theo ngu n n d phòng (SS); + H th ng bù Có kh n ng m r ng tùy nhu c u: + Panel hi n th tr ng thái c a máy phát n, thông s dòng n, dòng rò,…; + Thi t b giám sát dòng n t i dòng n dò, d dàng phát hi n l i dòng n dò; + Khóa chuy n đ i liên k t v i thi t b giao th c khác b ng thi t b I/O giao th c CAN; + Giao di n hình hi n th giá tr đo thông báo l i, thông s ho t đ ng; + K t n i d li u v i h th ng ki m soát u n HospEC b ng CAN-bus u m + Thi t k d ng module cho t b ng phân ph i, thi t b ch c n ng h th ng; + Thi t k t ng ph n (module), th c hi n l p đ t t ng ph n, d dàng l p đ t, qu n lý; + m b o an toàn, tiêu chu n không gian l p đ t; + C nh báo phát hi n s m l i dòng n rò, + An toàn cho ng v tr l i x y; i v n hành, ho t đ ng ...ON THE EXISTENCE OF POSITIVE SOLUTION FOR AN ELLIPTIC EQUATION OF KIRCHHOFF TYPE VIA MOSER ITERATION METHOD FRANCISCO J ´ ULIO S. A. CORR ˆ EA AND GIOVANY M. FIGUEIREDO Received 18 November 2005; Revised 11 April 2006; Accepted 18 April 2006 Dedicated to our dear friend and collaborator Professor Claudianor O. Alves We investigate the questions of existence of positive solution for the nonlocal problem −M(u 2 )Δu = f (λ,u)inΩ and u = 0on∂Ω,whereΩ is a bounded smooth domain of R N ,andM and f are continuous functions. Copyright © 2006 F. J. S. A. Corr ˆ ea and G. M. Figueiredo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is prop- erly cited. 1. Introduction In this paper, we study some questions related to the existence of positive solution for the nonlocal elliptic problem − M u 2 Δu = f (λ, u)inΩ, u = 0on∂Ω, (P) λ where Ω is a bounded smooth domain, M : R + → R is a function w hose behavior will be stated later, f : R + × R → R is a given nonlinear function, and ·is the usual norm in H 1 0 (Ω)givenby u 2 = |∇ u| 2 (1.1) and finally, through this work, u denotes the integral Ω u(x)dx. The main goal of this paper is to establish conditions on M and f under which prob- lem (P) λ possesses a positive solution. Problem (P) λ is called nonlocal because of the presence of the term M(u 2 ) which implies that the equation i n (P) λ is no longer a pointwise identity. This provokes some mathematical difficulties which make the study of such a problem particulary interesting. Hindawi Publishing Corporation Boundary Value Problems Volume 2006, Article ID 79679, Pages 1–10 DOI 10.1155/BVP/2006/79679 2 A Kirchhoff-type equation Besides, these kinds of problems have motivations in physics. Indeed, the operator M( u 2 )Δu appears in the Kirchhoff equation, by virtue of this ( P) λ ,iscalledofthe Kirchhoff type, which arises in nonlinear vibrations, namely, u tt − M u 2 Δu = f (x,u)inΩ × (0,T), u = 0on∂Ω × (0,T), u(x,0) = u 0 (x), u t (x,0) = u 1 (x) . (1.2) Hence, problem (P) λ is the stationary counterpart of the above evolution equation. Such a hyperbolic equation is a general version of the Kirchhoff equation ρ ∂ 2 u ∂t 2 − P 0 h + E 2L L 0 ∂u ∂x 2 dx ∂ 2 u ∂x 2 = 0 (1.3) presented by Kirchhoff [14]. This equation extends the classical d’Alembert’s wave equa- tion by considering the effects of the changes in the length of the strings during the vibra- tions. The parameters in (1.3) have the following meanings: L is the length of the string, h is the area of cross-section, E is the Young modulus of the material, ρ is the mass density and P 0 is the initial tension. Problem ( 1.2) began to call the attention of several researchers mainly after the work of Lions [15], where a functional analysis approach was proposed to attack it. The reader may consult [1, 2, 8, 16, 18] and the references therein, for more informa- tion on (P) λ . Actually, problem (P) λ is a particular example of a wide class of the so-called nonlocal equations whose study has deserved the attention of many researchers, mainly in recent years. Let us cite some nonlocal problems in order to emphasize the importance of their vi TABLE OF CONTENTS ACKNOWLEDGMENTS i ABSTRACT ii TÓM TẮT iv TÓM TẮT iv TABLE OF CONTENTS vi LIST OF FIGURES ix LIST OF TABLE x INTRODUCTION 1 1. Necessity of the thesis 1 2. Literature review 2 3. Objectives of the research 4 4. Research Methodology 5 5. Contribution of the thesis 8 6. Structure of the research 8 CHAPTER 1: THEORETICAL FOUNDATIONS 9 1.1. The concepts of service, customer service and service recovery 9 1.1.1. Service and customer service 9 1.1.2. Service recovery 10 1.2. Types of customer‟s response to the service failures 12 1.2.1. Types of customer actions 13 1.2.2. Types of complainers 13 vii 1.3. The reasons customers complain 14 1.4. The expectation of customers 15 1.4.1. Customers expectation of fair treatment 15 1.4.2. Companies‟ behavior 16 1.5. Service Recovery Strategies 17 1.5.1. Fail-safe your service – Do it right at the first time 18 1.5.2. Welcome and Encourage complaints 19 1.5.3. Act quickly 19 1.5.4. Treat customer fairly 21 1.5.5. Learn from recovery experiences 21 1.5.6. Learn from lost customers 21 1.5.7. Return to “Doing it right” 22 1.6. Service Guarantees 22 1.6.1. Benefits of Service Guarantees 23 1.6.2. Types of Service Guarantees 24 1.6.3. When to Use (or Not Use) a Guarantee 25 CHAPTER 2: SERVICE RECOVERY FOR TRADE FINANCE OPERATION IN VIETINBANK 26 2.1. Overview of VietinBank and trade finance operation 26 2.1.1. History of VietinBank 26 2.1.2. Corporate Vision, Mission, Values and Ambitions 28 2.1.3. Trade finance operation of VietinBank 29 2.1.4. VietinBank‟s Trade Finance resources 36 viii 2.2. Analysis of VietinBank‟s current situation of Service Recovery 39 2.2.1. How customers respond to service failures in VietinBank: 40 2.2.2. VietinBank‟s Service Recovery Strategies for Trade finance operation 44 2.2.3. VietinBank‟s Service Guarantees 49 2.3. Summary of strengths and weaknesses of service recovery activities in VietinBank 50 CHAPTER 3: RECOMMENDATIONS TO SERVICE RECOVERY FOR TRADE FINANCE OPERATION IN VIETINBANK 53 3.1. Strategies and solutions for the development of Trade finance operation in VietinBank 53 3.1.1. Quantitative targets: 53 3.1.2. Qualitative targets: 53 3.2. Strategies and actions plan for improvement of Service Recovery for trade finance operation in VietinBank 54 3.2.1. Strategy for improvement of Service Recovery for trade finance operation in VietinBank in the period of 2012-2017 54 3.2.2. Actions plan for improvement of Service Recovery for trade finance operation in VietinBank in the period of 2012-2017 60 3.1.3. Recommendations for the improvement of Service Recovery in VietinBank 72 REFERENCES 73 ANNEX LIST 75 ix LIST OF FIGURES Figure 1.1: Unhappy customers‟ repurchase intentions 11 Figure 1.2: Customer response following service failure 12 Figure 1.3: Types of failure respondents 14 Figure 1.4. Fairness and satisfaction 17 Figure 1.5. Service Recovery strategies 18 Figure 1.6: Causes behind service switching 22 Figure 2.1: VietinBank‟s Key Financial Index 29 Figure 2.2. Commercial banks in operation in Vietnam‟s market by 31 st Dec 2011 31 Figure 2.3: Vietnam Trade finance market shares 2010 32 Figure 2.4: Banks in Vietnam, with whom trade finance customers are transacting 34 Figure 2.5: Number of VietinBank‟s trade finance customers over 2008-2011 34 Figure 2.6: Duration (years) that customers transacting with VietinBank 36 Figure 2.7: The reasons customers do not complain 41 Figure 2.8: The reasons customers complain 42 Figure 2.9: The expectation of customers when complaining 42 Figure 2.10: Customer‟s identification of other complaining ways to a bank 45 Figure 2.11: Does VietinBank offer you service guarantees for trade finance? 50 x LIST OF TABLE Table 2.1: Summary of positive points and negative points of service recovery activities in VietinBank 51 Table 2.2 Strengths and weaknesses of service recovery activities in VietinBank . ... giám sát HospEC 2.7 Chu n truy n thông CAN bus 2.1 Module chuy n đ i ngu n cho t ph i phân Page of 22 Thi t b u n giám sát HospEC B nh nhân trung tâm c a m t b nh vi n ho c c s y t Vi c cung... tri n phân ph i b i Sigma Vietnam System JSC v i m c đích đ cung c p an toàn n b nh vi n ho c c s y t H th ng c a đáp ng yêu c u cao nh t v an toàn cung c p n t i b nh vi n ho c c s y t tuân theo... 60364-7-710:2002-11 DIN VDE 0100-710:2002-11 Gi i pháp c a HospEC H th ng u n giám sát HospEC đ c tích h p gi i pháp an toàn n h th ng n cung c p b nh vi n tin c y, hi u qu kinh t V i công ngh c a chúng