hirota bilinear method for nonlinear evolution equations

... Volterra operator In [3] the solutions of nonlinear and degenerate problems were investigated In general, existence of solutions for a class of nonlinear evolution equations of second order is proved ... the convergence of a finite volume scheme for the numerical solution for an elliptic–parabolic equation Using Rothe method, the author in [2] studied a nonlinear degenerate parabolic equation with ... and quantum mechanics can be described by doubly nonlinear problems The literature on the subject of local in time doubly nonlinear evolution equations is rather wide Among these contributions,...

Ngày tải lên: 21/06/2014, 17:20

... 10.5 B¨cklund transformation 159 a 10.6 Nonlinear superposition formula for Sawada-Kotera 160 10.7 Nonlinear superposition formula for Kaup-Kupershmidt ... References 167 X Contents Hirota bilinear method for nonlinear evolution equations Junkichi Satsuma ... B¨cklund transformation: definition and example 139 a Singularity analysis of nonlinear differential equations 139 4.1 Nonlinear ordinary differential equations ...

Ngày tải lên: 24/04/2014, 16:50

... 10.5 B¨cklund transformation 159 a 10.6 Nonlinear superposition formula for Sawada-Kotera 160 10.7 Nonlinear superposition formula for Kaup-Kupershmidt ... References 167 X Contents Hirota bilinear method for nonlinear evolution equations Junkichi Satsuma ... B¨cklund transformation: definition and example 139 a Singularity analysis of nonlinear differential equations 139 4.1 Nonlinear ordinary differential equations ...

Ngày tải lên: 24/04/2014, 16:50

... problem for Boltzmann equations: global existence and weak stability,” Annals of Mathematics, vol 130, no 2, pp 321–366, 1989 10 A Porretta, “Existence results for nonlinear parabolic equations ... Finite Elements for Reservoir Simulation, NorthHolland, Amsterdam, The Netherlands, 1986 W X Shen and S M Zheng, “Nonlocal initial-boundary value problems for nonlinear parabolic equations, ” Journal ... solution to the corresponding problem are well understood cf 1– , for the purpose, the Galerkin method was used For semilinear equations, the existence of global smooth solution was obtained in...

Ngày tải lên: 21/06/2014, 20:20

... iteration method for solving hyperbolic differential equations, ” International Journal of Nonlinear Sciences and Numerical Simulation, vol 8, no 3, pp 311– 314, 2007 J H He, “Variational iteration method a ... “Two methods for solving integral equations, ” Applied Mathematics and Computation, vol 77, no 1, pp 79–89, 1996 10 A M Wazwaz, “A reliable treatment for mixed Volterra-Fredholm integral equations, ” ... fixed point Also, putting L and α |λ|/3 shows that 1.1 holds for the nonlinear mapping T All of the conditions of Theorem 1.1 hold for the nonlinear mapping T and hence it is T -stable 6 Fixed Point...

Ngày tải lên: 21/06/2014, 20:20

... of the augmented Lagrangian method for nonlinear semidefinite programming,” Mathematical Programming, 2008 D Noll, “Local convergence of an augmented Lagrangian method for matrix inequality constrained ... “A global algorithm for nonlinear semidefinite programming,” SIAM Journal on Optimization, vol 15, no 1, pp 303–318, 2004 M Koˇ vara and M Stingl, “Pennon: a code for convex nonlinear and semidefinite ... that the importance of exploring numerical methods for solving nonlinear semidefinite programming problems has been recognized in the optimization community For instance, Koˇ vara and Stingl 3, have...

Ngày tải lên: 22/06/2014, 18:20

... control methods for singularly perturbed discrete bilinear systems, Pro[5] ceedings of the 4th Asian Control Conference, Singapore, September 2002, pp 670–675 12 Perturbation method for difference equations ... proposed method consists simply of writing the problem (Pε ) in a matrix form (see the proof of Theorem 2.1 for the details), and can be easily applied to initial value problems Our method is ... give proof of uniform convergence of the proposed iterative method Section is mainly devoted to validate the effectiveness of our method, compared with the singular perturbation method We consider...

Ngày tải lên: 22/06/2014, 22:20

... ) f (t,ex0 , ,exk ) > for t ∈ R and x0 , ,xk ≥ D, f (t,ex0 , ,exk ) < for t ∈ R and x0 , ,xk ≥ D, f (t,ex0 , ,exk ) < for t ∈ R and x0 , ,xk ≤ −D, f (t,ex0 , ,exk ) > for t ∈ R and x0 , ,xk ... differential equations with piecewise constant delays, J Math Anal Appl 99 (1984), no 1, 265–297 , A survey of differential equations with piecewise continuous arguments, Delay Differential Equations ... differential equations with piecewise constant argument deviations, Int J Math Math Sci (1983), no 4, 671–703 G Zhang and S S Cheng, Positive periodic solutions for discrete population models, Nonlinear...

Ngày tải lên: 23/06/2014, 00:20

... solutions for abstract semilinear evolution equations J Syst Sci Math Sci 25(6),720–728 (2005) 13 Li, Y: Existence of solutions to initial value problems for abstract semilinear evolution equations ... problems For evolution equations of integer order (a = 1), Li [12-16] and Yang [17] used this method, in which positive C0-semigroup play an important role The theory of impulsive differential equations ... iterative method for an initial value problem for ordinary differential equation Later on, many articles used the monotone iterative technique to establish existence and comparison results for nonlinear...

Ngày tải lên: 20/06/2014, 23:20

... exponents for heat equations with nonlinear flux boundary conditions on the boundary Israel J Math 94, 1250–146 (1996) Lin, ZG: Blowup behaviors for diffusion system coupled though nonlinear ... solution of exponential form for the scalar problem (1.4) with q2 = (p1 + 1)/2 (see [8]) Proof of Theorem 2.1 We consider solutions of form (2.1) Imposing that the porous equations (1.1) are fulfilled, ... are fulfilled Let us remark this parametric evolution comparison method to prove global nonexistence for arbitrary data first introduced in [20], for scalar quasilinear heat equation End of the...

Ngày tải lên: 21/06/2014, 00:20

... positive solutions for singular fractional equations Electron J Differ Equ 2008, 146:1-9 15 Zhang S: Positive solutions for boundary-value problems of nonlinear fractional differential equations Electron ... solutions for boundary value problems of nonlinear fractional differential equations Commun Nonlinear Sci Numer Simul 2011, 16:2086-2097 20 Yu Y, Jiang D: Multiple Positive Solutions for the Boundary ... coupled system of nonlinear fractional differential equations Appl Math Comput 2004, 150:611-621 25 Su X: Boundary value problem for a coupled system of nonlinear fractional differential equations Appl...

Ngày tải lên: 21/06/2014, 03:20

... Yıldırım, “Homotopy perturbation method for the nonlinear dispersive ¸ K m,n,1 equations with fractional time derivatives,” International Journal of Numerical Methods for Heat & Fluid Flow, vol 20, ... nonlinear equations The new homotopy perturbation method NHPM was applied to linear and nonlinear ODEs 17 In this paper, we construct the solution of system of fractional-order differential equations ... for different values of α, we will take advantage of the explicit formula 4.9 available for < α ≤ and consider the following two special cases Advances in Difference Equations Case Setting α form...

Ngày tải lên: 21/06/2014, 05:20

... solutions of fractional evolution equations, ” Chaos, Solitons and Fractals, vol 14, no 3, pp 433–440, 2002 M M El-Borai, “The fundamental solutions for fractional evolution equations of parabolic ... semilinear evolution equations, ” Nonlinear Analysis: Theory, Methods & Applications, vol 50, no 2, pp 173–189, 2002 26 H Liu and J.-C Chang, “Existence for a class of partial differential equations with ... no 1, pp 11–19, 1991 22 Z Fan, “Impulsive problems for semilinear differential equations with nonlocal conditions,” Nonlinear Analysis: Theory, Methods & Applications, vol 72, no 2, pp 1104–1109,...

Ngày tải lên: 21/06/2014, 05:20

... and F2 for nonlinearity f In addition, we only require that the nonlinear term f : J × X × X → X satisfies weak Carath´ odory condition: e for each u, v ∈ X, f ·, u, v is strongly measurable for ... Techniques for Nonlinear Differential Equations, vol 27 of Monographs, Advanced Texts and Surveys in Pure and Applied Mathematics, Pitman, Boston, Mass, USA, 1985 H.-Y Lan, “Monotone method for a system ... “Existence of solutions for anti-periodic boundary value problems of nonlinear impulsive functional integro-differential equations of mixed type,” Nonlinear Analysis: Theory, Methods & Applications,...

Ngày tải lên: 21/06/2014, 07:20

... Zennaro, Numerical Methods for Delay Differential Equations, Numerical Mathematics and Scientific Computation, Oxford University Press, Oxford, UK, 2003 Y Kuang, Delay Differential Equations with Applications ... perturbation parameter 17–20 In order to construct parameter-uniform numerical methods for singularly perturbed differential equations, two different techniques are applied Firstly, the fitted ... scheme 3.8 , to be ε-uniform convergent, we will use the fitted form of ωN,p This is a special non-uniform mesh which is condensed in the boundary layer The fitted special non-uniform mesh ωN,p on the...

Ngày tải lên: 21/06/2014, 07:20

... nonexistence theorems for nonlinear evolution equations, ” The Quarterly Journal of Mathematics Oxford, vol 28, no 112, pp 473–486, 1977 Z Yang, “Existence and asymptotic behaviour of solutions for a class ... damping and source terms,” Nonlinear Analysis: Theory, Methods & Applications, vol 56, no 6, pp 851–865, 2004 12 Z Yang, “Blowup of solutions for a class of non-linear evolution equations with non-linear ... solutions for some nonlinear hyperbolic equation with a nonlinear dissipative term,” Journal of Zhengzhou University, vol 29, no 3, pp 18–23, 1997 15 Y Ye, “On the decay of solutions for some nonlinear...

Ngày tải lên: 21/06/2014, 11:20

... subharmonics for nonlinear second order difference equations, ” Nonlinear Analysis: Theory, Methods & Applications, vol 67, no 6, pp 1737–1745, 2007 13 M Ma and Z Guo, “Homoclinic orbits for second ... second order differential equations, ” Journal of Differential Equations, vol 82, no 1, pp 15–27, 1989 W.-T Li, “Oscillation of certain second-order nonlinear differential equations, ” Journal of Mathematical ... max|F2 n, x | M2 |x|≤1 n −2 3.20 Take ω ∈ E such that |ω n | ⎧ ⎨1, for |n| ≤ 1, ⎩0, for |n| ≥ 2, 3.21 and |ω n | ≤ for |n| ∈ 1, For σ > 1, by Lemma 2.3 i and 3.21 , we have F1 n, σω n ≥ σμ n −1...

Ngày tải lên: 21/06/2014, 11:20

... domains,” Nonlinear Analysis: Theory, Methods & Applications, vol 69, no 1, pp 73–84, 2008 M Eduardo Hern´ ndez and S M Tanaka Aki, “Global solutions for abstract impulsive differential a equations, ” Nonlinear ... precompact for each i 2, 3, , p Therefore, {Qn2 u; u ∈ W} is precompact in PC 0, K , X , that is, the operator Qn2 : PC 0, K , X → PC 0, K , X is compact Advances in Difference Equations Thus, for ... holds Then, D Aα is a Banach space with the norm x α Aα x for x ∈ D Aα , T t : X → D Aα for t > 0, Aα T t x T t Aα x for x ∈ D Aα and t ≥ 0, for every t > 0, Aα T t is bounded on X and there exists...

Ngày tải lên: 21/06/2014, 11:20

... differential equations, ” Nonlinear Analysis: Theory, Methods & Applications, vol 72, no 3-4, pp 1604–1615, 2010 11 B Ahmad, “Existence of solutions for irregular boundary value problems of nonlinear ... 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 ... value problems for multi-term fractional differential equations, ” Journal of Mathematical Analysis and Applications, vol 345, no 2, pp 754–765, 2008 G M N’Gu´ r´ kata, “A Cauchy problem for some fractional...

Ngày tải lên: 21/06/2014, 16:20

... boundary value problems for impulsive differential equations and impulsive difference equations have received much attention [4–18] On the other hand, recently, the theory of dynamic equations on time ... solutions for first-order difference equation with impulses Int J Diff Equ 2, 225–239 (2006) [10] Nieto, JJ: Periodic boundary value problems for first-order impulsive ordinary diffeerential equations Nonlinear ... differential equations Nonlinear Anal Real World Appl 10, 680–690 (2009) [12] Nieto, JJ, Rodriguez-Lopez, R: Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations...

Ngày tải lên: 21/06/2014, 17:20