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Öğe A analytic and numerical solution to a modified Kawahara equation and a convergence analysis of the method(Elsevier Science Inc, 2006) Polat, Necat; Kaya, Dogan; Tutalar, H. IlhanIn this paper, we present an Adomian's decomposition method (shortly ADM) for numerical approximation traveling-wave solutions of the modified Kawahara equation. The numerical solutions are compared with the known analytical solutions. We also prove the convergence of Adomian decomposition method (ADM) applied to the modified Kawahara equation. (c) 2005 Elsevier Inc. All rights reserved.Öğe A analytic and numerical solution to a modified Kawahara equation and a convergence analysis of the method(Elsevier Science Inc, 2006) Polat, Necat; Kaya, Dogan; Tutalar, H. IlanIn this paper, we present an Adomian's decomposition method (shortly ADM) for numerical approximation traveling wave solutions of the modified Kawahara equation. The numerical solutions are compared with the known analytical solutions. We also prove the convergence of Adomian decomposition method (ADM) applied to the modified Kawahara equation. (c) 2006 Elsevier Inc. All rights reserved.Öğe Asymptotic behavior of a solution of the Cauchy problem for the generalized damped multidimensional Boussinesq equation(Pergamon-Elsevier Science Ltd, 2012) Polat, Necat; Piskin, ErhanThis work studies the Cauchy problem for the generalized damped multidimensional Boussinesq equation. By using a multiplier method, it is proven that the global solution of the problem decays to zero exponentially as the time approaches infinity, under a very simple and mild assumption regarding the nonlinear term. (C) 2012 Elsevier Ltd. All rights reserved.Öğe Blow up of a Solution for a System of Nonlinear Higher-Order Wave Equations with Strong Damping Terms(Amer Inst Physics, 2012) Polat, Necat; Piskin, ErhanThis work studies a initial-boundary value problem of the strong damped nonlinear higher-order wave equations. Under suitable conditions on the initial datum, we prove the blow up of the solution.Öğe Blow up of positive initial-energy solutions for a coupled nonlinear higher-order hyperbolic equations(Amer Inst Physics, 2015) Piskin, Erhan; Polat, NecatThis work studies an initial-boundary value problem of the coupled nonlinear higher-order hyperbolic equations with damping and source terms. Under suitable conditions on the initial datum, we prove the blow up of solutions with positive initial energy. We generalize some earlier results concerning the system.Öğe Blow up of solution for the generalized Boussinesq equation with damping term(Walter De Gruyter Gmbh, 2006) Polat, Necat; Kaya, DoganWe consider the blow up of solution to the initial boundary value problem for the generalized Boussinesq equation with damping term. Under some assumptions we prove that the solution with negative initial energy blows up in finite time.Öğe Blow-up phenomena and stability of solitary waves for a generalized Dullin-Gottwald-Holm equation(Springer, 2013) Dündar, Nurhan; Polat, NecatIn this work, we consider the Cauchy problem of the generalized Dullin-Gottwald-Holm equation. We establish a blow-up result for the generalized Dullin-Gottwald-Holm equation. In addition to this, we investigate the stability of solitary wave solutions of the equation.Öğe Doğrusal olmayan parabolik veya hiperbolik diferansiyel denklemlerde global çözümlerin yokluğu (Blow up)(2017) Polat, Necat; Tutalar, H. İlhan; Kaya, DoğanBu tezde, sınırdaki değerleri sıfır olan bazı parabolik ve hiperbolik tipten diferansiyel denklemler için başlangıç sınır değer problemlerinin çözümlerinin global yokluğu ele alınmıştır. İlk bölümde, blow up ile ilgili günümüze kadar yapılan çalışmalar tarihi gelişimiyle kısaca ele alınmıştır. Tezin sonraki bölümleri için gerekli olan temel bilgiler ikinci bölümde verilmiştir. Üçüncü bölümde, diferansiyel denklemlerde genellikle blow up olarak bilinen singularitenin oluşumu konusu ile ilgili bilgiler verilmiş ve blow up teorisi etrafında odaklanan klasik sorular ele alınmıştır. Dördüncü bölümde, sonlu zamanda global olmayan (blow up) çözüm ve çözümlerin büyümesi metotları üzerinde durulmuştur. Beşinci bölümde, damping terimli doğrusal olmayan bir dalga denkleminin bir sınıfı için başlangıç sınır değer probleminin çözümlerinin global yokluğu açık eşitsizlik metotları kullanılarak ispatlanmıştır. Altıncı bölümde, damping terimli Boussinesq denklemi için başlangıç sınır değer probleminin çözümlerinin global yokluğu açık eşitsizlik metotları kullanılarak ispatlanmıştır. Yedinci bölümde, damping terimli geliştirilmiş Boussinesq denklemi için başlangıç sınır değer probleminin çözümlerinin global yokluğu açık eşitsizlik metotları kullanılarak ispatlanmıştır. Sekizinci bölümde, doğrusal olmayan damping terimli doğrusal olmayan bir dalga denkleminin bir sınıfı için başlangıç sınır değer probleminin çözümlerinin global yokluğu açık eşitsizlik metotları kullanılarak ispatlanmıştır.Öğe Existence and Asymptotic Behavior of Solution of Cauchy. Problem for the Damped Sixth-order Boussinesq Equation(Springer Heidelberg, 2015) Polat, Necat; Piskin, ErhanWe consider the existence, both locally and globally in time, as well as the asymptotic behavior of solutions for the Cauchy problem of the sixth-order Boussinesq equation with damping term. Under rather mild conditions on the nonlinear term and initial data, we prove that the above-mentioned problem admits a unique local solution, which can be continued to a global solution, and the problem is globally well-posed. Finally, under certain conditions, we prove that the global solution decays exponentially to zero in the infinite time limit.Öğe Existence and Blow up of Solutions of the Cauchy Problem of the Generalized Damped Multidimensional Improved Modified Boussinesq Equation(Walter De Gruyter Gmbh, 2008) Polat, NecatWe consider the existence, both locally and globally in time, and the blow up of solutions of the Cauchy problem of the generalized damped multidimensional improved modified Boussinesq equation in W-s.p (R-n).Öğe Existence and blow-up of solution of Cauchy problem for the generalized damped multidimensional Boussinesq equation(Academic Press Inc Elsevier Science, 2009) Polat, Necat; Ertas, AbdulkadirWe consider the existence, both locally and globally in time, and the blow-up of solutions for the Cauchy problem of the generalized damped multidimensional Boussinesq equation. (C) 2008 Elsevier Inc. All rights reserved.Öğe Existence of Global Solutions for a Multidimensional Boussinesq-Type Equation with Supercritical Initial Energy(Amer Inst Physics, 2012) Taskesen, Hatice; Polat, NecatIn this work, global weak solutions of the multidimensional Boussinesq-type equation with power type nonlinearity gamma vertical bar u vertical bar(p), gamma > 0 and supercritical initial energy is given by potential well method. Classical energy methods can not guarantee the global existence for this type of nonlinearity. As is known the functional I (u) defined for potential well method includes only the initial displacement, and by use of sign invariance of this functional one can only prove the global existence for critical and subcritical initial energy. In the case of supercritical initial energy such a functional fails to prove the global existence. A new functional is defined, which contains not only initial displacement, but also initial velocity.Öğe Existence of Local Solution for a Double Dispersive Bad Boussinesq-Type Equation(Amer Inst Physics, 2012) Dundar, Nurhan; Polat, NecatThis work studies a purely spatial higher order bad Boussinesq-type equation. The local existence of the solution was given by aid of contraction mapping principle.Öğe Existence results for a nonlinear Timoshenko equation with high initial energy(Amer Inst Physics, 2015) Taskesen, Hatice; Polat, NecatThe aim of the present paper is to study the initial -boundary value problem for a nonlinear Timoshenko equation with high energy initial data. Existence of global weak solutions is proved by sign preserving property of a new functional which is introduced for the potential well method.Öğe Existence, Asymptotic Behaviour, and Blow up of Solutions for a Class of Nonlinear Wave Equations with Dissipative and Dispersive Terms(Walter De Gruyter Gmbh, 2009) Polat, Necat; Kaya, DoganWe consider the existence, both locally and globally in time, the asymptotic behaviour, and the blow up of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative and dispersive terms. Under rather mild conditions on the nonlinear term and the initial data we prove that the above-mentioned problem admits a Unique local solution, which call be continued to I global solution, and the solution decays exponentially to zero as t -> + infinity. Finally, under a suitable condition oil the nonlinear term, we prove that the local solutions with negative and nonnegative initial energy blow up in finite time.Öğe Existence, global nonexistence, and asymptotic behavior of solutions for the Cauchy problem of a multidimensional generalized damped Boussinesq-type equation(Tubitak Scientific & Technological Research Council Turkey, 2014) Piskin, Erhan; Polat, NecatWe consider the existence, both locally and globally in time, the global nonexistence, and the asymptotic behavior of solutions for the Cauchy problem of a multidimensional generalized Boussinesq-type equation with a damping term.Öğe Exponential Decay and Blow up of a Solution for a System of Nonlinear Higher-Order Wave Equations(Amer Inst Physics, 2012) Piskin, Erhan; Polat, NecatThis work studies a initial-boundary value problem of the weak damped nonlinear higher-order wave equations. Under suitable conditions on the initial datum, we prove that the solution decays exponentially and blows up with negative initial energy.Öğe Global existence and asymptotic behavior of a solution of Cauchy problem for a viscous Cahn Hilliard type equation(2013) Polat, Necat; Dündar, NurhanViskoz Cahn-Hillard tipi denklem için Cauchy probleminin çözümünün asimptotik davranışı ve zaman boyunca local ve global olarak varlığını ele aldık. Nonlineer terim ve başlangıç koşulları üzerinde oldukça hafifletilmiş koşullar altında yukarıda bahsedilen problemin tek lokal çözümü olduğunu ve bununda global çözüme ilerletilebileceğini ispatladık ve problem global olarak iyi-konulmuştur. Son olarak, belirli kesin şartlar altında global çözümün sonsuza doğru gidilirken üstsel olarak sıfıra doğru azaldığını ispatladık.Öğe Global existence and decay of solutions for the generalized bad Boussinesq equation(Zhejiang Univ, Editorial Committee Applied Mathematics, 2013) Taskesen, Hatice; Polat, Necat; Ertas, AbdulkadirIn this paper, we consider the global existence of solutions for the Cauchy problem of the generalized sixth order bad Boussinesq equation. Moreover, we show that the supremum norm of the solution decays algebraically to zero as (1 + t)(-(1/7)) when t approaches to infinity, provided the initial data are sufficiently small and regular.Öğe Global existence for a double dispersive sixth order Boussinesq equation(2013) Polat, Necat; Taşkesen, HaticeBu makalede altıncı mertebeden çift dispersif terimli Boussinesq denkleminin ?
