self similar solutions of nonlinear diffusion equations2

... + λuβ = Exact Similarity Solutions of Nonlinear PDEs 3.1 Reduction of PDEs by Infinitesimal Transformations 3.2 Systems of Partial Differential Equations 3.3 Self- Similar Solutions of the Second ... the nature of self- similar solutions of the first and second kind More importantly, Barenblatt brought out manifestly the role of these solutions as intermediate asymptotics; these solutions not ... with the help of many examples the place of similarity solutions in the general solution Exact similarity solutions via group theoretic methods and the direct similarity approach of Clarkson and...

Ngày tải lên: 24/04/2014, 17:09

... existence of positive solutions of 3.17 will not be guaranteed in this case Proof of Theorem 3.2 We only prove i ii can be proved by a similar method To study the existence of positive solutions of ... we study the existence of one-sign solutions of the nonlinear problem x f t, x , t ∈ 0, T , 1.18 x x T , x x T The proofs of the main results are based on the properties of G and the Dancer’s ... result concerning the global structure of the set of positive solutions of parameterized nonlinear operator equations, which is essentially a consequence of Dancer 12, Theorem Suppose that E...

Ngày tải lên: 21/06/2014, 11:20

... classical solutions twice continuously differentiable solutions in the pointwise sense of G ≤ on relatively open subset of O are solutions of G− ≤ Suppose, moreover, that whenever u is a solution of ... 2 Boundary Value Problems the proof of existence of viscosity solutions of first-order Hamilton-Jacobi equations, Crandall et al had applications of Perron’s Method to second-order partial ... viscosity solutions of Hamilton-Jacobi equations,” Communications on Pure and Applied Analysis, vol 6, no 2, pp 389–410, 2007 D Nunziante, “Uniqueness of viscosity solutions of fully nonlinear...

Ngày tải lên: 21/06/2014, 20:20

... Journal of Mathematical Analysis and Applications, vol 295, no 2, pp 378–391, 2004 15 R Ma and N Castaneda, “Existence of solutions of nonlinear m-point boundary-value problems,” Journal of Mathematical ... Wei, and F Xu, “The existence of countably many positive solutions for a system of nonlinear singular boundary value problems with the p-Laplacian operator,” Journal of Mathematical Analysis and ... at least two positive solutions u1 and u2 Motivated by the above papers, the purpose of our paper is to show the existence of twin or an arbitrary odd number of positive solutions to the BVP...

Ngày tải lên: 21/06/2014, 20:20

... result than that of Theorem 3.2, that is, under the assumption of asymptotic almost periodicity of a bounded solution of 2.7 , he showed the existence of an almost periodic solution of the limiting ... “Periodic solutions of nonlinear integrodifferential equations,” Tohoku Mathematical Journal, vol 41, no 1, pp 105–116, 1989 Y Song and H Tian, “Periodic and almost periodic solutions of nonlinear ... limiting equations of integrodifferential equations,” Funkcialaj Ekvacioj, vol 33, no 2, pp 345–362, 1990 10 M N Islam, “Almost periodic solutions of nonlinear integral equations,” Nonlinear Analysis:...

Ngày tải lên: 22/06/2014, 11:20

... that operator (2.29) is nonlinear Mutual comparability of solutions of (1.1) The aim of this section is to establish certain conditions under which each two solutions of (1.1) lying in a certain ... assumptions of Corollary 3.4, one of the following two conditions is true: (a) A preserves the K-negligibility of elements of the set Π; (b) A is continuous in the topology of X Then all the solutions of ... obvious that the set of solutions of problem (4.27), (4.28) coincides with that of the continuous solutions of (1.1), where λ = and b(t) := c + t a q(s)ds, t ∈ [a,b] (4.31) 24 Journal of Inequalities...

Ngày tải lên: 22/06/2014, 18:20

... “Blow-up of solutions of nonlinear wave equations in three space dimensions,” Manuscripta Mathematica, vol 28, no 1–3, pp 235–268, 1979 [6] S G Georgiev, “Blow up of the solutions of nonlinear ... lim u t →0 L2 ([0,∞)) = ∞ (3.62) Svetlin Georgiev Georgiev 23 Proof of Theorem 1.2 4.1 Local existence of nontrivial solutions of nonhomogeneous Cauchy problem (1), (2) In this section we will ... prove that (1 ) has unique nontrivial solution ω(r) ∈ L2 ([0,1)) Proof of Theorem 1.1 3.1 Local existence of nontrivial solutions of homogeneous Cauchy problem (1), (2) In this section, we will prove...

Ngày tải lên: 22/06/2014, 19:20

... existence of periodic solutions of discrete difference equations, Uzbekski˘ ı Matematicheski˘ Zhurnal (1995), no 3, 88–90 (Russian) ı [10] Kh Turaev, On the existence and uniqueness of periodic solutions ... research was supported by the Kamea Fund of the Israel Ministry of Science and Technology References [1] S S Cheng and G Zhang, Positive periodic solutions of a discrete population model, Functional ... assume that the evolution operator of (4.4) satisfy the inequality Rs (V (T,0)) < In addition, suppose that (rν + μ)m(W,T) < r (4.8) Periodic solutions of nonlinear vector difference equations...

Ngày tải lên: 22/06/2014, 22:20

... periodic solutions of every odd period larger than one The results presented in this paper extend previous ones of Etheridge and Rodriguez [4] who studied the existence of periodic solutions of difference ... component function of G maps each boundary point of Ω into Ω itself and then, by breaking up the boundary of Ω into separate pieces, consider the effect of the first component function of G on those ... of A−T is A−T itself, so that I − A−T N = −1 −1 (A.18) For a solution of (2.14), then, x(0) must be a real constant multiple of (A.19) It follows that solutions of (2.14) are of the form x(t)...

Ngày tải lên: 23/06/2014, 00:20

... i ∂x i ⎦ Ω i =1 Ω ⎣ i =1 which completes the proof of the lemma N ∫ ∑ a i ( x, ∇u k ) Trang 22 TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 9, SỐ -2006 Proof of Theorem 3.1 By Lemma 3.1, there exists a sequence ... Topological degree for a class of operators and applications, Nonlinear Analysis 57, 505-518, (2004) [5] M.A Krasnosel´kii, Topological methods in the theory of nonlinear integral equations, Pergamon ... mapping of class ( S )+ Suppose that ∈ D \ ∂D and Au ≠ , Au, u ≥ for u ∈ ∂D Then deg ( A, D, ) = Proposition 2.3 Let A t : D → X* , t ∈ [ 0,1] be the homotopy family of operators of class...

Ngày tải lên: 22/07/2014, 10:21

... 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 ... purpose of this paper is to investigate the asymptotic behavior of the time-dependent solution of (1.1) in relation to constant steady-state solutions, including regions of attraction of the stable ... boundary condition is of Neumann type as that in (1.1) then constant steady-state C.V Pao / Nonlinear Analysis 48 (2002) 349 – 362 351 solutions can often be found from the nonlinear reaction function...

Ngày tải lên: 29/10/2015, 14:19

... condition for the boundedness of all solutions of (1.1) and the scalar case of (1.1), respectively The next result provides a sufficient condition for the boundedness of solutions of (1.1) Theorem 4.1 Let ... boundedness of the solutions in nonlinear discrete Volterra difference equations Istv´n Gy˝ri∗1 and Essam Awwad1,2 a o Department of Mathematics, Faculty of Information Technology, University of Pannonia, ... has been an increasing interest in the study of the asymptotic behavior of the solutions of both convolution and non-convolution-type linear and nonlinear Volterra difference equations (see [1–17]...

Ngày tải lên: 20/06/2014, 20:20

... Existence of positive solutions for nonlinear m-point boundary value problems on time scales Junfang Zhao∗1 , Hairong Lian1 and Weigao Ge2 School of Mathematics and Physics, China University of Geosciences, ... value problems of ordinary differential equations (BVPs for short) arise in a variety of different areas of applied mathematics and physics For example, the vibrations of a guy wire of a uniform ... and 1000 Existence of at least two positive solutions In this section, we will apply fixed point Theorem 2.5 to prove the existence of at least two positive solutions to the nonlinear BVP (1.6)...

Ngày tải lên: 20/06/2014, 20:20

... Uniform decay of solutions for a quaslinear system of viscoelastic equations Nonlinear Anal 71, 2257–2267 (2009) doi:10.1016/j.na.2009.01.060 22 Agre, K, Rammaha, MA: Systems of nonlinear wave ... (2006) 23 Said-Houari, B, Messaoudi, SA, Guesmia, A: General decay of solutions of a nonlinear system of viscoelastic wave equations Nonlinear Diff Equ Appl (2011) 24 Muñoz Rivera, JE: Global solution ... (2006) doi:10.1016/j.jmaa.2005.07.022 13 Song, HT, Zhong, CK: Blow-up of solutions of a nonlinear viscoelastic wave equation Nonlinear Anal RWA 11, 3877–3883 (2010) doi:10.1016/j.nonrwa.2010.02.015...

Ngày tải lên: 21/06/2014, 00:20

... uniqueness of solutions for coupled systems of higher-order nonlinear fractional differential equations Fixed Point Theory Appl 2010, 2010:1-17 30 Babakhani A: Positive solutions for system of nonlinear ... (u, v) Î C[0, 1] × C[0, 1] is a solution of (1.1) if and only if (u, v) Î C[0, 1] × C[0, 1] is a solution of system (3.1) This proof is similar to that of Lemma 3.3 in [25], so is omitted From ... is continuous in view of continuity of G(t, s), f(t, u), and g(t, u) For any bounded set M, T (M) is uniformly bounded and equicontinuous This proof is similar to that of Lemma 2.1.1 in [20],...

Ngày tải lên: 21/06/2014, 03:20

... β−1 ds y τ dτ − λu s s−τ Γ β β−1 ds 2.7 y τ dτ − λu s ds Proof Similar to the discussion of 9, equation 1.5 , the general solution of C Dβ C Dα λ ut y t 2.8 can be written as t ut t − s α−1 Γ ... Province, and the Construct Program of the Key Discipline in Hunan Province References A Alsaedi, “Existence of solutions for integrodifferential equations of fractional order with antiperiodic ... conditions,” International Journal of Differential Equations, vol 2009, Article ID 417606, pages, 2009 B Ahmad, “Existence of solutions for fractional differential equations of order q ∈ 2, with antiperiodic...

Ngày tải lên: 21/06/2014, 05:20

... stability of the zero solution and estimates of the zero solution and the estimates of the rate of decay of solutions to second order wave equations are obtained Similar results for the higher-order nonlinear ... polynomial decay rate for solutions is established There are many articles devoted to the investigation of the asymptotic behavior of solutions of nonlinear wave equations with nonlinear dissipative ... 1993 V K Kalantarov and A Kurt, “The long-time behavior of solutions of a nonlinear fourth order wave equation, describing the dynamics of marine risers,” Zeitschrift fur Angewandte Mathematik...

Ngày tải lên: 21/06/2014, 07:20

... papers 1–3, 11–14 , the authors studied the existence of periodic solutions, subharmonic solutions, and homoclinic solutions of some special forms of 1.1 by using the critical point theory These papers ... function u∗ is a desired classical solution of 1.1 Since d > 0, u∗ is a nontrivial homoclinic solution The proof is complete Proof of Theorem 1.2 In the proof of Theorem 1.1, the condition that F2 ... that I u ≥ α, that is, assumption ii of Lemma 2.1 holds The proof of Theorem 1.2 is completed 14 Advances in Difference Equations Proof of Theorem 1.4 In view of Lemma 2.4, I ∈ C1 E, R We first...

Ngày tải lên: 21/06/2014, 11:20

... from λ1 a0 , λ1 a0 × {0} in R × E Proof of the Main Results Proof of Theorem 1.5 It is clear that any solution of 2.30 of the form 1, u yields solutions u of 1.1 We will show that C crosses the ... δ2 } It is easy to check that, for < δ < δ, all of the conditions of Theorem A are satisfied So there exists a connected component Cn of solutions of 2.30 containing an , bn × {0}, and either i ... solution of the problem λf t, u Lu 2.21 Since λf t, u t ≥ for a.e t ∈ 0, , Lemma 2.2 yields u t ≥ for t ∈ 0, Thus, u is a nonnegative solution of 2.19 , and the closure of the set of nontrivial solutions...

Ngày tải lên: 21/06/2014, 11:20

... uniqueness of mild solutions to impulsive fractional differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol 72, no 3-4, pp 1604–1615, 2010 11 B Ahmad, “Existence of solutions ... on 0, Conclusions This paper studies the existence and uniqueness of solutions for nonlinear integro-differential equations of fractional order q ∈ 1, with three-point nonlocal fractional boundary ... C, vol 2, pp 189–205, 2008 13 B Ahmad and J J Nieto, “Existence of solutions for nonlocal boundary value problems of higherorder nonlinear fractional differential equations,” Abstract and Applied...

Ngày tải lên: 21/06/2014, 16:20