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Öğe Analysis of thermoelastic laminated Timoshenko beam with time-varying delay(Elsevier B.V., 2024) Founas, Besma; Yazid, Fares; Djeradi, Fatima Siham; Ouchenane, Djamel; Pişkin, Erhan; Boulaaras, SalahThis document presents a study into a linear thermoelastic laminated Timoshenko beam featuring a time-varying delay. Utilizing the semigroup method and the variable norm technique, we establish the well-posedness of the system. Subsequently, leveraging the energy method under appropriate conditions, we demonstrate the system's exponential stability.Öğe Blow up and decay of solutions for a Klein-Gordon equation with delay and variable exponents(Wiley Blackwell, 2023) Yüksekkaya, Hazal; Pişkin, ErhanIn this article, we deal with a Klein-Gordon equation with delay and variable exponents. Under appropriate conditions, we establish the blow up of solutions in a finite time. Also, we get the decay results utilizing the Komornik integral inequality.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 global existence of solution for a riser problem with logarithmic nonlinearity(Yıldız Technical University, 2021) Irkıl, Nazlı; Pişkin, ErhanIn this work, we analyze the influence of the logarithmic source term on solutions to quasilinear riser equation. Firstly, we prove blow up results. Later, we obtain that solutions are global 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 AT INFINITY OF WEAK SOLUTIONS FOR A HIGHER-ORDER PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY(Gökhan ÇUVALCIOĞLU, 2021) Cömert, Tuğrul; Pişkin, ErhanThe main goal of this work is to study the inital boundary value problem for a higher-order parabolic equation with logarithmic source term u_{t}+(-\Delta )^{m}u=uln (u). We obtain blow-up at infinity of weak solutions, by employing potential well technique. This improves and extends some previous studies.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 A blow up of solutions for a system of Klein-Gordon equations with variable exponent. Theoretical and Numerical Results(Polish Mathematical Society, 2023) Gözen, Sedanur Mazı; Okutmuştur, Baver; Pişkin, Erhan; Yılmaz, NebiIn this paper, we consider a system of Klein-Gordon equations with variable exponents. The first part of the manuscript is devoted to the proof of the blow up of solutions with negative initial energy under suitable conditions on variable exponents and initial data. The theoretical part is supported by numerical experiments based on P1-finite element method in space and the BDF and the Generalized-alpha methods in time illustrated in the second part. The numerical and analytical results of the blow up solutions agree with each other.Öğe Blow up of the higher-order kirchhoff-type system with logarithmic nonlinearities(Wiley Blackwell, 2023) Irkıl, Nazlı; Pişkin, Erhan; 0000-0001-6587-4479This contribution investigates the solution of high-order Kirchhoff-type system with logarithmic nonlineraities. Under the appropriate assumptions, we establish the global nonexistence of the solution at low initial energy level E (0) < d.Öğe Blow-up of solutions for a logarithmic quasilinear hyperbolic equation with delay term(Univ. Prithtines, 2021) Pişkin, Erhan; Yüksekkaya, HazalIn this work, we deal with a logarithmic quasilinear hyperbolic equation with delay term. Under suitable conditions, we get blow up of solutions in a finite time. Our results are more general than the earlier results.Öğe BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY(Gökhan ÇUVALCIOĞLU, 2021) Yüksekkaya, Hazal; Pişkin, ErhanIn this paper, we consider a nonlinear viscoelastic plate equation with distributed delay. Under suitable conditions, we obtain the blow-up of solutions with distributed delay and source terms.Öğe Decay and Blow up of Solutions for a Delayed Wave Equation with Variable-Exponents(Murat TOSUN, 2020) Pişkin, Erhan; Yüksekkaya, HazalThis work deals with a nonlinear wave equation with delay term and variable exponents. Firstly, we prove the blow up of solutions in a finite time for negative initial energy. After, we obtain the decay results by applying an integral inequality due to Komornik. These results improve and extend earlier results in the literature. Generally, time delays arise in many applications. For instance, it appears in physical, chemical, biological, thermal and economic phenomena. Moreover, delay is source of instability. A small delay can destabilize a system which is uniformly asymptotically stable. Recently, several physical phenomena such as flows of electro-rheological fluids or fluids with temperature-dependent viscosity, nonlinear viscoelasticity, filtration processes through a porous media and image processing are modelled by equations with variable exponents.Öğe Doğrusal olmayan evolüsyon denklemlerin çözümlerinin azalması ve patlaması(2015) Pişkin, ErhanBu tezin ilk bölümünde çözümlerin azalması ve patlaması ile ilgili günümüze kadar yapılan çalışmalar tarihi gelişimiyle ele alınmıştır. İkinci bölümde tez boyunca kullanılacak olan temel tanım, teorem ve eşitsizlikler verilmiştir. Üçüncü bölümde tezde kullanılan çözümlerin azalması ve patlaması ile ilgili lemmalar ispatları ile birlikte verilmiştir. Dördüncü bölümde doğrusal olmayan damping ve kaynak terim içeren dalga denklem sisteminin çözümlerinin lokal varlığı, global varlığı, enerji azalması ve patlaması çalışılmıştır. Beşinci bölümde yüksek mertebeden zayıf damping terimli denklem sisteminin çözümlerinin enerji azalması ve patlaması çalışılmıştır. Altıncı bölümde ise güçlü damping, doğrusal olmayan damping ve kaynak terim içeren doğrusal olmayan yüksek mertebeden denklem sisteminin çözümlerinin global varlığı, enerji azalması ve patlaması çalışılmıştır.Öğe Doğrusal olmayan hiperbolik kısmi diferansiyel denklemlerin çözümlerinin matematiksel davranışı(2017) Pişkin, Erhan; Polat, NecatBu tezde doğrusal olmayan hiperbolik tipten bazı kısmi diferansiyel denklemlerin çözümlerinin matematiksel davranışı incelenmiştir. İlk bölümde, hiperbolik kısmi diferansiyel denklemlerle ilgili günümüze kadar yapılmış çalışmalar tarihi gelişimi ile kısaca ele alınmıştır. İkinci bölümde, tezin sonraki bölümleri için gerekli olan temel bilgiler verilmiştir. Üçüncü bölümde, ikinci mertebeden hiperbolik denklemlerin zayıf çözümleri tanımlanmıştır. Dördüncü bölümde, dördüncü mertebeden dispersive ve dissipative terimli bir dalga denkleminin asimptotik davranışı incelenmiştir. Beşinci bölümde, damping terimli altıncı mertebeden bir Cauchy probleminin lokal ve global varlığı, başlangıç verilerine sürekli bağımlılığı ve asimptotik davranışı ispatlanmıştır.Öğe Energy decay and blow-up of solutions for a class of system of generalized nonlinear Klein-Gordon equations with source and damping terms(TUBITAK, 2023) Çelik, Zeynep Sümeyye; Gür, Şevket; Pişkin, ErhanIn this work, we investigate generalized coupled nonlinear Klein-Gordon equations with nonlinear damping and source terms and initial-boundary value conditions, in a bounded domain. We obtain decay of solutions by use of Nakao inequality. The blow up of solutions with negative initial energy is also established.Öğe Energy Decay of Solutions for a System of Higher-Order Kirchhoff Type Equations(Naim ÇAĞMAN, 2019) Pişkin, Erhan; Harman, EzgiIn this work, we considered a system of higher-order Kirchhoff type equations with initial and boundary conditions in a bounded domain. Under suitable conditions, we proved an energy decay result by Nakao's inequality techniques.Öğe Existence and asymptotic behavior of beam-equation solutions with strong damping and p(x)-biharmonic operator(B.Verkin Institute for Low Temperature Physics and Engineering of the NAS of Ukraine, 2022) Ferreira, Jorge; Panni, Willian S.; Messaoudi, Salim A.; Pişkin, Erhan; Shahrouzi, MohammadIn this paper, we consider a nonlinear beam equation with a strong damping and the p(x)-biharmonic operator. The exponent p(·) of nonlinearity is a given function satisfying some condition to be specified. Applying Faedo– Galerkin’s method, the existence of weak solutions is proved. Using Nakao’s lemma, the asymptotic behavior of weak solutions is established with mild assumptions on the variable exponent p(·). We show the asymptotic behavior of the weak solution is exponentially and algebraically depending on the variable exponent. This work improves and extends many other results in the literature.Öğe Existence and blow up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities(Texas State University, 2021) Antontsev, Stanislav; Ferreira, Jorge; Pişkin, ErhanIn this article, we consider a nonlinear plate (or beam) Petrovsky equation with strong damping and source terms with variable exponents. By using the Banach contraction mapping principle we obtain local weak solutions, under suitable assumptions on the variable exponents p(.) and q(.). Then we show that the solution is global if p(.) >= q(.). Also, we prove that a solution with negative initial energy and p(.) < q(.) blows up in finite time.Öğe Existence and blow up of solutions of a viscoelastic m(x)-biharmonic equation with logarithmic source term(University of Miskolc, 2024) Butakın, Gülistan; Pişkin, ErhanIn this paper, we are concerned with a logarithmic nonlinear viscoelastic m(x)-biharmonic equation. Firstly, we proved the local existence of solutions by using the Faedo-Galerkin method. Later, we proved the blow up of solutions by using the concavity method.
