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Öğe Blow up and exponential growth to a kirchhoff-type viscoelastic equation with degenerate damping term(Murat TOSUN, 2023) Ekinci, Fatma; Pişkin, ErhanIn this paper, we consider a Kirchhoff-type viscoelastic equation with degenerate damping term have initial and Dirichlet boundary conditions. We obtain the blow up and exponential growth of solutions with negative initial energy.Öğe Blow up and exponential growth to a petrovsky equation with degenerate damping(Emrah Evren KARA, 2021) Ekinci, Fatma; Pişkin, ErhanThis paper deals with the initial boundary value problem of Petrovsky type equation with degenerate damping. Under some appropriate conditions, we study the finite time blow up and exponential growth of solutions with negative initial energy.Öğe Blow up and growth of solutions to a viscoelastic parabolic type Kirchhoff equation(University of Nis, 2023) Pişkin, Erhan; Ekinci, FatmaIn this article, we study a system of viscoelastic parabolic type Kirchhoff equation with multiple nonlinearities. We obtain a finite time blow up of solutions and exponential growth of solution with negative initial energy.Öğe Blow up of Solutions for a Coupled Kirchhoff-type Equations with Degenerate Damping Terms(Prairie View A & M Univ, Dept Mathematics, 2019) Piskin, Erhan; Ekinci, FatmaIn this paper, we investigate a system of coupled Kirchhoff-type equations with degenerate damping terms. We prove a nonexistence of global solutions with positive initial energy. Later, we give some estimates for lower bound of the blow up time.Öğe Blow up of solutions for a parabolic equation of Kirchhoff-type with multiple nonlinearities(Batman Üniversitesi, 2020) Pişkin, Erhan; Ekinci, FatmaIn this paper, we investigated a class of doubly nonlinear parabolic systems with Krichhoff-type. We prove a blow up of solutions with negatif initial energy.Öğe Blow up, exponential growth of solution for a reaction-diffusion equation with multiple nonlinearities(Tbilisi Centre Math Sci, 2019) Piskin, Erhan; Ekinci, FatmaIn this paper, we consider a reaction diffusion equation with multiple nonlinearities. We prove a blow up and exponential growth of solution with negative initial energy. Our new results generalizes and improves earlier results.Öğe Dejenere sönüm terimli evolüsyon denklemlerin çözümlerinin davranışı(Dicle Üniversitesi, Fen Bilimleri Enstitüsü, 2021) Ekinci, Fatma; Pişkin, ErhanBu tezin ilk bölümünde fen ve mühendislik gibi uygulamalı bilimlerde ortaya çıkan evolüsyon denklemlere kısaca değinilmiştir. Ayrıca nitel davranış (qualitative theory) ile ilgili kısa bir bilgi verilmiştir. İkinci bölümde dejenere sönüm terimli denklemler, Kirchhoff tipli denklemler ve Timoshenko denklemleri ile ilgili günümüze kadar yapılan çalışmaların tarihi gelişimi ele alınmıştır. Üçüncü bölümde tez boyunca kullanılacak olan temel tanım, lemma ve eşitsizlikler verilmiştir. Ayrıca Kirchhoff ve Timoshenko denklemlerinin modellenmesi ve Galerkin yaklaşım metodu verilmiştir. Dördüncü bölüm ise tezin orijinal kısmı olup üç kısımdan oluşmaktadır. İlk kısımda dejenere sönüm terimli Timoshenko denkleminin çözümlerinin patlaması çalışılmıştır. İkinci kısımda dejenere sönüm terimli Kirchhoff tipli denklem sisteminin çözümlerinin azalması ve patlaması çalışılmıştır. Son kısımda ise dejenere sönüm terimli viskoelastik dalga denklem sisteminin çözümlerinin varlığı ve patlaması çalışılmıştır.Öğe Existence, blow up and growth of solutions for a coupled quasi-linear viscoelastic Petrovsky equations with degenerate damping terms(Analytic Publ. Co., 2021) Ekinci, Fatma; Pişkin, Erhan; Zennir, KhaledWe consider a quasilinear coupled system of two viscoelastic equations with degenerate damping and source terms under Dirichlet boundary condition. We obtain the global existence, blow up and exponential growth of solutions under some restrictions on the initial data, relaxation functions and degenerate damping terms.Öğe Exponential Growth and Lower Bounds for the Blow-up Time of Solutions for a System of Kirchhoff-type Equations(Tokat Gaziosmanpasa University, 2019) Pişkin, Erhan; Ekinci, Fatma; Butakın, VeyselThis paper deals with the system of Kirchhoff-type equations with a bounded domain ??R?. We prove exponential growth of solutions with negative initial energy. Later, we give some estimates for lower bounds of the blow up time.Öğe Exponential growth of solutions for a parabolic system(Batman Üniversitesi, 2019) Ekinci, Fatma; Pişkin, ErhanIn this paper, we investigated the initial boundary problem of a class of doubly nonlinear parabolic systems. We prove exponential growth of solution with negative initial energy.Öğe General decay and blowup of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms(Wiley, 2019) Pişkin, Erhan; Ekinci, Fatma; 0000-0001-6587-4479In this work, we consider a nonlinear system of viscoelastic equations of Kirchhoff type with degenerate damping and source terms in a bounded domain. Under suitable assumptions on the initial data, the relaxation functions g(i)(i = 1, 2) and degenerate damping terms, we obtain global existence of solutions. Then, we prove the general decay result. Finally, we prove the finite time blow-up result of solutions with negative initial energy. This work generalizes and improves earlier results in the literature.Öğe Global Existence and General Decay of Solutions for a Quasilinear System with Degenerate Damping Terms(Hindawi Ltd, 2021) Ekinci, Fatma; Piskin, Erhan; Boulaaras, Salah Mahmoud; Mekawy, IbrahimIn this work, we consider a quasilinear system of viscoelastic equations with degenerate damping, dispersion, and source terms under Dirichlet boundary condition. Under some restrictions on the initial datum and standard conditions on relaxation functions, we study global existence and general decay of solutions. The results obtained here are generalization of the previous recent work.Öğe Global Existence and General Decay of Solutions for Quasilinear System with Degenerate Damping Terms(Murat TOSUN, 2020) Pişkin, Erhan; Ekinci, FatmaIn this work, we investigate a quasilinear system of two viscoelastic equations with degenarete damping, dispersion and source terms under Dirichlet boundary conditions. Under suitable conditions on the relaxation function $h_{i}$ $\left( i=1,2\right)$ and initial data, we establish global existence and general decay results. This work generalizes and improves earlier results in the literature.Öğe Growth of solutions for fourth order viscoelastic system(Yıldız Technical University, 2021) Ekinci, Fatma; Pişkin, ErhanWe consider a system of viscoelastic equations with degenerate damping and source terms under Dirichlet boundary condition. We prove the exponential growth of solutions under some restrictions on the initial data, relaxation functions and degenerate damping termsÖğe Local Existence and Blow Up of Solutions for a Coupled Viscoelastic Kirchhoff-Type Equations with Degenerate Damping(Murat TOSUN, 2020) Pişkin, Erhan; Ekinci, FatmaIn this paper, we consider the initial boundary value problem of a coupled viscoelastic Kirchhofftype equations with degenerate damping. Firstly, we prove a local existence theorem by using the Faedo-Galerkin approximations. Then, we study blow up of solutions when initial energy is possitive.Öğe Local existence and blow up solutions for a coupled viscoelastic Kirchhoff-type equation with degenerate damping(Univ Miskolc Inst Math, 2021) Pişkin, Erhan; Ekinci, FatmaIn this paper, we consider the initial boundary value problem of a coupled viscoelastic Kirchhoff-type equations with degenerate damping: {u(tt) - M(parallel to del u parallel to(2)) Delta u+ integral(t)(0) mu(1)(t - s) Delta(s)ds + |u|k +|v|l|ut|p-1ut=f1(u,v), vtt-M(parallel to del v parallel to 2) Delta u+ integral(t)(0) mu 2(t - s) increment v(s)ds + |v|theta +|u|rho |vt|q-1vt=f2(u,v). Firstly, we prove a local existence theorem by using the Faedo-Galerkin approximations. Then, we study blow up of solutions when initial energy is positive.Öğe Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms(Serbian Society of Mechanics, 2020) Pişkin, Erhan; Ekinci, Fatma; Zennir, KhaledIn this paper, we investigate a nonlinear system of viscoelastic equations with degenerate damping and source terms in a bounded domain. Under appropriate assumptions on the parameters, degenerate damping terms and the relaxation functions i, (= 1, 2), we prove local existence and uniqueness of the solution by using the Faedo-Galerkin method with a new scenario. Then, we prove the blow-up of weak solutions to problem (1.1). This improves earlier results in the literatureÖğe NONEXISTENCE AND GROWTH OF SOLUTIONS FOR A PARABOLIC p-LAPLACIAN SYSTEM(Yildiz Technical Univ, 2019) Piskin, Erhan; Ekinci, FatmaIn this paper, we investigate the initial boundary problem of a class of doubly nonlinear parabolic systems. We prove a nonexistence of global solutions and exponential growth of solution with negative initial energy.Öğe NONEXISTENCE OF GLOBAL SOLUTIONS FOR COUPLED KIRCHHOFF-TYPE EQUATIONS WITH DEGENERATE DAMPING TERMS(Mathematical Research Press-Math Res, 2018) Piskin, Erhan; Ekinci, FatmaIn this paper, we investigate a system of coupled Kirchhoff-type equations with degenerate damping terms. We prove the nonexistence of global solutions with positive initial energy. We also give some estimates for lower bound of the blow up time.Öğe Qualitative analysis of solutions for a Kirchhoff-type parabolic equation with multiple nonlinearities(Hacettepe University Faculty of Science, 2021) Pişkin, Erhan; Ekinci, FatmaIn this work, the local and global existence of weak solutions by using the Faedo-Galerkin method, the finite time blow up of the weak solution with positive initial energy and the general decay of the solution are discussed. Finally, we consider the exponential growth of the solution with sufficient conditions. This work generalizes and improves earlier results in the literature, see [L.X. Truong and N. Van Y, On a class of nonlinear heat equations with viscoelastic term, Comput. Math. Appl., 2016] and [L.X. Truong and N. Van Y, Exponential growth with L p -norm of solutions for nonlinear heat equations with viscoelastic term, Appl. Math. Comput., 2016].
