solutions of the diffusion equation

... 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 ... /xn ,” Journal of Mathematical Analysis and Applications, vol 233, no 2, pp 790–798, 1999 18 K S Berenhaut and S Stevi´ , ? ?The behaviour of the positive solutions of the difference equation c xn

Ngày tải lên: 21/06/2014, 20:20

... classifications of the path equation for the different forms of arbitrary function of the governing equation [3–7] Based on Noether’s theorem, if Noether symmetries of an ordinary differential equation ... terms of first order derivative of 𝑦 To write equation of (51) in terms of the reduced equation of 𝑤, we can obtain the firstorder derivative the solution of (59) and we can write (51) equation ... forms of 𝑓(𝑦) Then the application of (18) to (14) and separation with respect to powers of 𝑦󸀠 and arranging yield the set of determining equations, the over-system of partial differential equations

Ngày tải lên: 02/11/2022, 10:47

... Consequently, the operator L : M → M is contractive operator We note that the set M is closed subset of the space Ꮿ((0,1]L2 ([0, ∞))) (for the proof see Lemma A.1 in the appendix of this ... Consequently, the operator R : M → M is contractive operator We note that the set M is closed subset of the space Ꮿ((0,1]L2 ([0, ∞))) (for the proof see Lemma A.1 in the appendix of this ... up of the solutions of homogeneous Cauchy problem (1), (2) Let v(t) be the same function as in Theorem 3.1 Theorem 3.2 Let n ≥ 2 be fixed,... (H7) we have lim F = +0 t →0 (3.61) Therefore

Ngày tải lên: 22/06/2014, 19:20

... to thickness of double layer and (4) the dielectric constant of the medium is the same everywhere in the liquid In the EDL theory, the local concentrations of cations, C+(x) and of anions, C−(x) ... respect to distance x from the solid surface computed using the solutions of the linearized and nonlinear PB equation 3.1 The distribution of (x) The variation of the electric potential (x) ... analytical solution to the nonlinear PB equation needs to be considered Additionally, to the best of my knowledge the difference in the zeta potential calculation between the solutions of the linearized

Ngày tải lên: 04/02/2021, 20:09

... completes the proof In the theorem below we study local and global bifurcations of nonconstant solutions of system 3.7 from the set of constant solutions The idea of proof is natural We compute the ... the proof of Lemma 3.2 the study of ker T± is equivalent to the study of solutions of the following system: −Δφ1 λk0 ± −Δφ2 φ1 , 3.12 From condition 3.11 it follows that the linear space of solutions ... the Euler ring of the group S1 , see 19, 20 For the convenience of the reader, one has reminded the definition of the Euler ring of the groups S1 in appendix It is a known fact that change of

Ngày tải lên: 01/11/2022, 08:55

... the asymptotics of the solutions. .. n→∞ (4.10) Thus, the limiting equation is exactly the linearized equation (4.1), and an application of Poincar´ ’s theorem completes the proof of ... characteristic equation of the linearized equa- tion evaluated at the equilibrium. The results on asymptotics of (1.2), (1.3), and (1.4)will show all the complexity of the asymptotics of the general equation ... (1.18) Now the proof follows as the proof of [7, Theorem 1.4.8].  The next two theorems give precise information about the asymptotics of linear non- autonomous difference equations. Consider the scalar

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 8.InSection 4, the main results are formulated, in Sections 5–7 the proofs of the main ... Consequently, the direct application of the method of [21] is not possible. The history of the motion equation from (1.1) is given in details in [21]. On the basis of the rheological relation of Jeffreys-Oldroyd ... equation, approximation of the equation in a weak sense and application of the topological theory of a degree that allows to establish the existence of solutions on the basis of a priori estimates

Ngày tải lên: 23/06/2014, 00:20

... investigate the problem of the existence or nonexistence of global solutions of the Cauchy characteristic problem in the light cone of the future. 1. Statement of the problem Consider a nonlinear wave equation ... by virtue of (3.10), the function u is the solution of (3.12), and according to the unique solvability of that equation, u = v ≥ 0 in the domain DT Thus the proof of Lemma 3.3 ... bounded below by a lig ht cone of the future S ∞ with the vertex at the origin and above by the light cone of the past S − x 0 ,t 0 : t =t 0 −|x −x 0 | with the vertex at the point (x 0 ,t 0 ). Lemma

Ngày tải lên: 23/06/2014, 00:20

... C = const On the Smoothness of Solutions 145 For j = we obtain the statement Propostion 2.2 is proved We can now state our theorem on the smoothness of generalized solutions of the problem (2.1) ... ∂ k apq q D ∂tk By Theorem 2.1 the function v = uts still satisfies the boundary conditions Therefore from inductive hypothesis and by repeating arguments of the proof in the case s = 0, we obtain ... infinite cylinder Ω∞ = Ω×(0, ∞) was given in [5] The o aim of this paper is to establish some theorems on the smoothness of generalized solutions of the problem in domains with conical points on

Ngày tải lên: 06/08/2014, 05:20

... steady-state solutions One of the di culties is the lack of explicit information about the steady-state solutions of the corresponding elliptic boundary-value problem when the boundary condition is of ... ˆ c˜ then c ≤ u(x) ≤ c on The conclusion if u(x) is a solution of (2.14) in the sector c; of the theorem follows from Theorem 3.2 of [13] (see also [12]) When the time delay Ji ∗ ui is either ... The stability conditions for these model problems are given in terms of the rate constants of the reaction function and is independent of the time delays and the e ect of di usion Global existence

Ngày tải lên: 29/10/2015, 14:19

... positive integer The equation (1) is called the modified generalized regularized long wave (mGRLW) equation If μ = 0, the equation (1) is called the generalized regularized long wave (GRLW) Equation ... work, we consider the solution of the mGRLW equation uÞ + uò + uỏ uò uòò uòòị = 0, x ∈ :a, b;, t ∈ :0, T;, with the initial condition u x, = f x , x ∈ :a, b;, (1) (2) and the boundary condition ... the present method is a successful numerical technique for solving the GRLW equations and the mGRLW equations Keyword: mGRLW equation; septic B-spline; collocation method; finite difference Email:

Ngày tải lên: 13/01/2020, 09:24

... interrupt the work of the department  Advantages in regional management Then the organizational chart of the Customer care department is expected to be as follows: Flow chart The organization of customer ... the whole customer system of company Therefore, the number of employees does not need much Hence, for the period from year 2018 to year 2019 the organization chart of the Customer care department ... care service of the company Base on these research results, the author provide some solutions to improve quality of DCL’s customer care services such as systematize customer data of the company;

Ngày tải lên: 17/03/2021, 17:26

... test examples, and the numerical results have been compared with the exact solutions The and in the solutions show the efficiency of the method computationally Keywords: MRLW equation; quartic ... SOLUTION OF THE MRLW EQUATION Nguyen Van Dung1, Nguyen Viet Chinh2 Hanoi National University of Education Hanoi Metropolitan University Abstract: In this paper, numerical solutions of the modified ... engineering [1]. In? ?the? ?past several years, many different methods have been used to estimate  the? ?solution? ?of? ?the? ?MRLW? ?equation,  for example, see [1, 3].  In  this  present work, we  have  applied? ?the? ?quartic 

Ngày tải lên: 28/06/2021, 19:39

... in the research that in addition to the improvement of the quality of education, measures such as strengthening management of and improving the quality of cultural activities, focusing on the ... Analysis of A Professionalism Scale in Pharmacy, Journal of Social and Administrative Pharmacy, Vol 6, No 1, 1989, pp 31-38 [18] W W Chin, P A Todd, On the Use, Usefulness, and Ease of Use of Structural ... VNU Journal of Science: Economics and Business, Vol 37, No (2021) 9-20 Original Article Application of the Structure Equation Model Impacts of Socio-economic Changes on Poverty

Ngày tải lên: 04/04/2022, 10:40

... estimates for solutions of the BVP problem Nevertheless, we present a proof of the uniqueness result in the last section of the paper The outline of the paper is as follows: section details the non-existence ... can now turn to the proof of the theorem It ponders on the previous construction and on the use of the closed graph theorem We refer to Lax [8] for similar arguments in the context of geometric ... of Theorem 1.3 : we skip it for the sake of brevity The proof of these spacial results are again based on construction of an unstable quasimode for the linearized operator It turns out that the

Ngày tải lên: 19/10/2022, 09:55

... estimates for solutions of the BVP problem Nevertheless, we present a proof of the uniqueness result in the last section of the paper The outline of the paper is as follows: section details the non-existence ... can now turn to the proof of the theorem It ponders on the previous construction and on the use of the closed graph theorem We refer to Lax [8] for similar arguments in the context of geometric ... of Theorem 1.3 : we skip it for the sake of brevity The proof of these spacial results are again based on construction of an unstable quasimode for the linearized operator It turns out that the

Ngày tải lên: 19/10/2022, 11:18

... and the refractive indices of the two waves are given by the lengths of the semi–axes of this ellipse and the directions of these semi–axes give the directions of * o  * e  oscillations of the ... between the light direction m and the direction of light energy transfer P (the Poynting vector) According to [2], [3] the angle  of the lack of coincidence between the light direction m and the ... tests: * The orthogonality of D* o and D* e via their scalar multiplication * The orthogonalities D* o m  D* e m  * The normalized conditions of vectors D* o and D* e The lack of the

Ngày tải lên: 18/02/2023, 06:44

... given in the next section We give the definition of solutions to the nonhomogeneous A-harmonic equation and the obstacle problem In the mean time, we show some properties of their solutions Then, ... we introduce the obstacle problem about the nonhomogeneous A-harmonic equation Then, we prove the existence and uniqueness of solutions to the nonhomogeneous A-harmonic equation and the obstacle ... prove the existence and uniqueness of solutions to the Dirichlet problem for the nonhomogeneous A-harmonic equation with Sobolev boundary values Let ℝn be the real Euclidean space with the dimension

Ngày tải lên: 20/06/2014, 22:20

... and give a proof of Theorem 2.4 The solutions are in fact given as limits of smooth solutions of appropriate approximate equations and we may assume for our estimates that the solutions under ... 15] and give the Proof of Theorem 2.5 Hence, we only consider the estimate of u ∞ for the smooth solution u(t) of (3.1) As above, let C, Cj be the generic constants independent of k and i Denote ... initial data u0 (x) is small under the assumptions of Theorems 2.7 and 2.8 Also, we derive the asymptotic behavior of solution u(t) Proof of Theorem 2.7 The existence of solution for (1.1) in small

Ngày tải lên: 21/06/2014, 20:20

... measure on the moments of jumps < s1 < · · · < sn < t of the derivatives of the paths q(.) and of the n copies of the measure M on the values q(sj ) of the paths at these moments In other words, ... the sense of L2 -convergence As the convergence of the solutions of (0·25) to the solutions of the ordinary Schrăodinger equation (0Ã6) (similar to (0Ã19)) seems to be unknown, the use of (0·25) ... om The starting point for the present study is the representation to the solutions of the Schrăodinger equation with a potential being the Fourier transform of a finite measure in terms of the

Ngày tải lên: 30/01/2020, 21:59