fundamental solutions of the creeping flow equations

... but also the fact that they are themselves solutions to a similar system of equations This allowed us to improve the exponent s, needed √ in the proof of well-posedness of equations of type (6),8 ... of the Main Theorem with the exception of those results which concern the asymptotic properties of the Ricci coefficients (the Asymptotics Theorem), and the straightforward modifications of the ... desired in the proof of (93) The remaining term on the left-hand side of (93) is easier to treat Proof of the L2 − L∞ decay estimate; Theorem 2.1 In this section we rely on the Boundedness Theorem...

Ngày tải lên: 16/02/2014, 05:20

... results of If we put σ these theorems, the same results as Theorem in are obtained in We will prove Theorem 1.1 a and b in Sections and 4, respectively The proof of Theorem 1.2 is included in the ... 373–390, 1993 R Suzuki, “Existence and nonexistence of global solutions of quasilinear parabolic equations, ” Journal of the Mathematical Society of Japan, vol 54, no 4, pp 747–792, 2002 C Bandle, ... is called the critical exponent On the other hand, 6–9 and so on study the inhomogeneous equations i.e., f x / ≡ in 1.1 Bandle et al study the case m 1, σ 0, and Zeng and Zhang study the case...

Ngày tải lên: 21/06/2014, 11:20

... behavior of solutions of the system of difference equations xn+1 = a + xn c + yn e + zn , yn+1 = , zn+1 = b + yn d + zn f + xn In [8], Özban studied the positive solutions of the system of rational ... rational difference equations xn+1 = yn−k , yn+1 = yn xn−m yn−m−k In [9], Zhang et al investigated the behavior of the positive solutions of the system of the difference equations xn = A + yn−p ... behavior of a three-dimensional linear fractional system of difference equations J Math Anal Appl 310, 673–689 (2005) Özban, AY: On the positive solutions of the system of rational difference equations...

Ngày tải lên: 20/06/2014, 22:20

... mentioning that the conditions of our theorems are easily to verify, so they are applicable to a variety of problems, see Examples 4.1 and 4.2 The proof of our main results is based upon the following ... t∈[η,1] β(1 − η) , η} − βη Proof Note that u“ (t) ≤ 0, by applying the concavity of u, the proof is easy So we omit it where γ = min{βη, Proofs of main theorems Define the operator T : C[0, 1] ® ... aspects of these equations are yet to be explored For some recent work on equations of fractional order with deviated arguments, see [46-48] and the references therein In this article, we consider the...

Ngày tải lên: 21/06/2014, 03:20

... differential equations, ” Bulletin of the Institute of Mathematics Academia Sinica, vol 13, no 4, pp 367– 384, 1985 20 N Parhi and S Parhi, “On the behaviour of solutions of the differential equations ... ¸ of the Greek Mathematical Society, vol 39, pp 131–137, 1997 26 C Tunc and E Tunc, “On the asymptotic behavior of solutions of certain second-order differential ¸ ¸ equations, ” Journal of the ... nonpositive Journal of Inequalities and Applications Nonoscillation Behaviors of Solutions of 1.1 In this section, we obtain sufficient conditions for the nonoscillation of solutions of 1.1 Theorem 2.1...

Ngày tải lên: 22/06/2014, 02:20

... if 1.16 holds true, then we have u Lq ≤C u r/q Lr u 1−r/q , ˙0 B∞,∞ ≤ r < q < ∞ 1.21 Proof of Theorem 1.2 This section is devoted to the proof of Theorem 1.2 First, we recall the following result ... Applied Mathematics, vol 41, no 4, pp 437–458, 1988 6 Journal of Inequalities and Applications H Sohr and W von Wahl, “On the regularity of the pressure of weak solutions of Navier-Stokes equations, ” ... regularity of weak solutions of the Navier-Stokes system,” Journal of Differential Equations, vol 62, no 2, pp 186–212, 1986 M Struwe, “On partial regularity results for the Navier-Stokes equations, ”...

Ngày tải lên: 22/06/2014, 02:20

... i 1, The proof of a is complete b In virtue of Lemma 5.5 the proof of the theorem will be complete if we show that the sequences H and h satisfy the conditions H2 – H5 in Section Since the series ... of solutions of difference Volterra equations, ” Applied Mathematics Letters, vol 16, no 6, pp 857–862, 2003 18 Z H Li, The asymptotic estimates of solutions of difference equations, ” Journal of ... some lemmas Lemma 5.1 The hypotheses of Theorem 3.1 imply that the hypotheses of Theorem A are satisfied, and hence the solution z : z n n≥0 of 3.1 , 3.2 is bounded Proof Let > be such that ρ W is...

Ngày tải lên: 22/06/2014, 11:20

... solution of a fourth-order algebraic matrix equation is required during the derivation of the bounds, and the numerical aspect has not been discussed In the present paper, we derive the bounds of solutions ... defined in the statement of the theorem Finally, from (2.20) and (2.22), we get (2.17) The proof is completed Theorem 2.8 If there exist an SPD matrix X and a constant ε > satisfying the linear ... positive definite solutions P to (1.1) and P < X The proof is completed Remark 2.9 From the relations between the solution of the perturbed discrete Lyapunov equation and that of an appropriate...

Ngày tải lên: 22/06/2014, 22:20

... completes the proof of the proposition Behavior of the positive solutions of fuzzy equation (1.1) In this section, we study the behavior of the positive solutions of (1.1) Firstly, we study the periodicity ... uniqueness of the positive solutions of fuzzy difference equations (1.1) and (1.2) In this section, we study the existence and the uniqueness of the positive solutions of the fuzzy difference equations ... use the following technique: we investigate the behavior of the solutions of a related family of systems of two parametric ordinary difference equations and then, using these results and the fuzzy...

Ngày tải lên: 23/06/2014, 00:20

... By this the proofs of the part of the results (which require the rather long proofs) are given in Section In Section 4, the main results are formulated, in Sections 5–7 the proofs of the main ... respect to γk ¯ The definition of the L-condensing map is given in [3] The proof of theorem repeats the proof of Theorem 2.2 in [21] on the strength of ¯ ¯ Lemmas 5.6–5.8 and the inequality u ... [17]), and γn is the operator of taking of the normal component of a trace on the boundary of a function defined on Ω0 The operator γn 236 On weak solutions of the equations of motion 1/2 is...

Ngày tải lên: 23/06/2014, 00:20

... 8 Numerical Solutions of the Black Scholes Equation The left-hand side of the heat equation, on the other hand, cannot be unambiguously approximated The following are some of the more common ... exponentials of the first column Note that the S values in this grid correspond to those of the Jarrow– Rudd scheme of Figure 7.4 If the reader is unsure of the reason for this, he will find the answer ... the initial values at t = and work across the grid towards the point (N, M) But because of the simple way in which the u n+1 only depend on the adjacent values to the m immediate left, only solutions...

Ngày tải lên: 25/10/2013, 19:20

... by the standard deviation of the actual P&L; and  The variance of the unexplained P&L divided by the variance of the actual P&L The specific time period that would be used in the computation of ... design of the regime also contributed to, and amplified, the problems exposed during the crisis These include:  The role of the regulatory boundary: The Committee believes that its definition of the ... address the shortcomings of the framework As a result, the Committee initiated a fundamental review of the trading book regime, beginning with an assessment of “what went wrong” The fundamental...

Ngày tải lên: 17/02/2014, 03:20

... the categories of unity of the form of the will (its universality), plurality of the matter (the objects, i.e., the ends), and totality of the system of these In forming our moral judgement of ... beings On the other hand, that which merely contains the ground of possibility of the action of which the effect is the end, this is called the means The subjective ground of the desire is the spring, ... the conception of an object within the reach of our faculties can exercise on the will of the subject, in consequence of its natural properties, depends on the nature of the subject, either the...

Ngày tải lên: 07/03/2014, 04:20

... under the Agreement II (“Verständigung II”) and are under the sole ownership of the Federal States On the basis of the public legal framework and under the ownership of the Federal States, they ... are owned either by the municipalities and/or savings banks associations, on the one hand, or by the Federal States on the other Therefore, the separation of responsibilities within the savings ... the weaknesses of one side with the strengths of the other The tie-up is aimed rather at securing – by means of balanced business and balance sheet structures – a structural contribution to the...

Ngày tải lên: 15/03/2014, 10:20

... vacuum solutions 29.1 Twisting vacuum solutions – the field equations 29.1.1 The structure of the field equations 29.1.2 The integration of the main equations 29.1.3 The remaining field equations ... Exact Solutions of Einstein’s Field Equations A revised edition of the now classic text, Exact Solutions of Einstein’s Field Equations gives a unique survey of the known solutions of Einstein’s ... surprise for the reader may lie in the enormous number of known exact solutions Those who not work in the field often suppose that the 1.2 The development of the subject intractability of the full...

Ngày tải lên: 24/04/2014, 17:07

... vacuum solutions 29.1 Twisting vacuum solutions – the field equations 29.1.1 The structure of the field equations 29.1.2 The integration of the main equations 29.1.3 The remaining field equations ... Exact Solutions of Einstein’s Field Equations A revised edition of the now classic text, Exact Solutions of Einstein’s Field Equations gives a unique survey of the known solutions of Einstein’s ... surprise for the reader may lie in the enormous number of known exact solutions Those who not work in the field often suppose that the 1.2 The development of the subject intractability of the full...

Ngày tải lên: 24/04/2014, 17:07

... carried out the mathematical calculations, participated in the interpretations of the results and drafted the manuscript JJAG conceived of the study, participated in the analysis of the results ... precedence of the heat flux vector to the temperature gradient at all In fact, whether the heat flux vector precedes the temperature gradient or not depends on the combined effects of the thermal ... the difference of the time delays t = tq-tT These studies have pointed out that the usefulness of the Cattaneo-Vernotte and DPL exact models is limited In this study, by means of the method of...

Ngày tải lên: 21/06/2014, 04:20

... and they give rise to many applications see Not only the new theory of the so-called “dynamic equations unifies the theories of differential equations and difference equations but also extends these ... G ut p τ Δτ ≤ G u T 2.53 P T The rest of the proof is similar to that of Theorem 2.8, and the details are omitted The proof is completed Theorem 2.10 Assume that the function f t, u0 , , un−1 ... discrete analysis The cases when a time scale is equal to the real numbers or to the integers represent the classical theories of differential and of difference equations Many other interesting...

Ngày tải lên: 21/06/2014, 05:20

... multiple of k On the other hand, in the remaining two cases, the study of the regular variation of the solutions gives the additional information that the positive solutions, even if they are ... M∞,0 The above theorem shows how the study of the regular variation of the solutions and the M-classification supplement each other to give an asymptotic description of nonoscillatory solutions ... SV \ NSV The main properties of regularly varying sequences, useful to the development of the theory in the subsequent sections, are listed in the following proposition The proofs of the statements...

Ngày tải lên: 21/06/2014, 11:20

... 2.7 The proof of Lemma 2.3 is completed Main Results In this section, we investigate the boundedness of solutions of 1.1 Let q > p > 1, and let {xn }∞ −1 be a positive solution of 1.1 with the ... for any n ≥ Let S be the set of all initial values x−1 , x0 ∈ 0, ∞ × 0, ∞ such that the positive solutions {xn }∞ −1 of 1.1 are bounded Then we have the following theorem n Theorem 3.6 S ∞ n Qn ... follows 16 Theorem A If p q ≤ 1, then the zero equilibrium of 1.1 is globally asymptotically stable If q 1, then the equilibrium x p of 1.1 is globally asymptotically stable If < q < p, then every...

Ngày tải lên: 21/06/2014, 20:20