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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 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 Damping terimli Timoshenko denkleminin çözümlerinin patlaması(Dicle Üniversitesi, Fen Bilimleri Enstitüsü, 2018) Yüksekkaya, Hazal; Pişkin, ErhanBu tezin ilk bölümünde fen ve mühendislik gibi uygulamalı bilimlerde ortaya çıkan diferansiyel denklemlere kısaca değinilmiş ve çözümlerin patlaması ile ilgili temel bilgiler verilmiştir. İkinci bölümde damping terimli Timoshenko denklemi ile ilgili yapılan çalışmalar özetlenmiştir. Üçüncü bölümde diferansiyel denklemler, fonksiyonel analiz ve Sobolev uzayları ile ilgili temel kavramlar ve bazı eşitsizlikler verilmiştir. Daha sonra çözümlerin patlamasını ispatlarken kullandığımız lemmalar verilmiştir. Dördüncü bölümde, önce kiriş teorileri ile ilgili tanımlar verilmiştir. Daha sonra Timoshenko denkleminin modellenmesi verilmiştir. Son kısım ise tezin orijinal kısmı olup çözümlerin patlaması negatif, sıfır ve pozitif başlangıç enerjileri için ispatlanmıştır.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 Existence, decay, and blow-up of solutions for a higher-order Kirchhoff-type equation with delay term(Hindawi LTD, 2021) Yüksekkaya, Hazal; Pişkin, Erhan; Boulaaras, Salah Mahmoud; Cherif, Bahri BelkacemThis article deals with the study of the higher-order Kirchhoff-type equation with delay term in a bounded domain with initial boundary conditions, where firstly, we prove the global existence result of the solution. Then, we discuss the decay of solutions by using Nakao's technique and denote polynomially and exponentially. Furthermore, the blow-up result is established for negative initial energy under appropriate conditions.Öğe Existence, nonexistence, and stability of solutions for a delayed plate equation with the logarithmic source(Hindawi Limited, 2021) Yüksekkaya, Hazal; Pişkin, Erhan; Boulaaras, Salah Mahmoud; Cherif, Bahri Belkacem; Zubair, Sulima AhmedIn this work, we study a plate equation with time delay in the velocity, frictional damping, and logarithmic source term. Firstly, we obtain the local and global existence of solutions by the logarithmic Sobolev inequality and the Faedo-Galerkin method. Moreover, we prove the stability and nonexistence results by the perturbed energy and potential well methods.Öğe Gecikmeli terim içeren hiperbolik tipten denklemlerin çözümlerinin matematiksel davranışı(Dicle Üniversitesi, Fen Bilimleri Enstitüsü, 2022) Yüksekkaya, Hazal; Pişkin, ErhanGecikmeli terim içeren denklemler ilk olarak 18. yüzyılda Bernoulli kardeşler ve Leonard Euler tarafından ele alınmışlardır. Bu denklemlerin sistematik olarak çalışılmaya başlanması ise 1940 da Myshkis ve Bellman tarafından başlanmıştır. Zaman gecikmeleri genellikle termal, ekonomik olaylar, biyolojik, kimyasal ve fiziksel gibi birçok farklı problemde ortaya çıkar. Birçok durumda, gecikme bir kararsızlık kaynağıdır ve hatta gelişigüzel küçük bir gecikme bile, ek koşullar veya kontrol şartları kullanılmadığı sürece, normal bir gecikme olmaksızın da düzgün, asimptotik olarak kararlı olan bir sistemin dengesini bozabilir. Ancak bazı denklemler için gecikmenin varlığı dengeleyici bir etkiye sahip olabilir. Bu nedenle, zaman gecikmeli denklemlerin, kararlılık analizi ve sağlam kontrolü teorik ve pratik öneme sahiptir. Bu tezin ilk bölümünde fen ve mühendislik gibi uygulamalı bilimlerde ortaya çıkan gecikmeli terim içeren denklemlere kısaca değinilmiştir. İkinci bölümde gecikmeli terim içeren denklemlerle ile ilgili günümüze kadar yapılan çalışmalar tarihi gelişimi ele alınmıştır. Üçüncü bölümde tez boyunca kullanılacak olan temel tanım, lemma, teorem ve eşitsizlikler verilmiştir. Dördüncü bölüm iki altbölümden oluşmaktadır. Dördüncü bölümün ilk kısmında gecikmeli terim içeren, p(x)-Laplacian tipli değişken üslü denklemin çözümlerinin patlaması ve azalması; ikinci kısmında ise gecikmeli terim içeren, değişken üslü viskoelastik dalga denkleminin çözümlerinin varlığı ve patlaması çalışılmıştır. Beşinci bölüm iki altbölümden oluşmaktadır. Beşinci bölümün ilk kısmında dağılımlı gecikmeli terim içeren logaritmik Kirchhoff tipli denklemin çözümlerinin global varlığı, azalması ve patlaması; ikinci kısmında ise gecikmeli terim içeren logaritmik dalga denkleminin çözümlerinin lokal varlığı, global varlığı ve azalması çalışılmıştır. Altıncı bölümde, gecikmeli terim içeren, polinomal kaynak terime sahip, bir yüksek mertebeden Kirchhoff tipli denklemin çözümlerinin varlığı, azalması ve patlaması ispatlanmıştır. Yedinci bölümde ise, dağılımlı gecikmeli terim içeren bir viskoelastik Kirchhoff sisteminin çözümlerinin üstel büyümesi çalışılmıştır.Öğe General energy decay estimate for a viscoelastic dampedswelling porous elastic soils with time delay(John Wiley and Sons Ltd., 2023) Yüksekkaya, Hazal; Pişkin, Erhan; al-Mahdi, Adel M.; Kafini, Mohammad M.This paper is concerned with the viscoelastic damped swelling porous elastic soils with time delay. Under more general assumption on the relaxation function and some specific conditions on the weight of the delay, we establish general decay results by using multiplier method and some properties of convex functions. These results generalize and improve some earlier related results in the literature.Öğe Global attractors for the higher-order evolution equation(Walter de Gruyter GMBH, 2020) Pişkin, Erhan; Yüksekkaya, HazalIn this paper, we obtain the existence of a global attractor for the higher-order evolution type equation. Moreover, we discuss the asymptotic behavior of global solution.Öğe Local existence and nonexistence of global solutions for a plate equation with time delay(Yıldız Technical University, 2021) Yüksekkaya, Hazal; Pişkin, ErhanIn this article, we study a plate equation with frictional damping, nonlinear source and time delay. Firstly, we establish the local existence by using the semigroup theory. Then, under suitable conditions, we prove the nonexistence of global solutions for positive initial energy. Time delays often appear in many practical problems such as thermal, economic phenomena, biological, chemical, physical, electrical engineering systems, mechanical applications and medicine.Öğe Local existence, global existence and decay results of a logarithmic wave equation with delay term(Wiley, 2023) Yüksekkaya, Hazal; Pişkin, ErhanIn this article, we deal with a logarithmic wave equation with strong damping and delay. Firstly, we prove the local existence by utilizing the semigroup theory. Later, we obtain the global existence of solutions by using the well-depth method. Moreover, under appropriate assumptions on the weight of the delay and that of strong damping, we get the exponential decay.Öğe NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY(Gökhan ÇUVALCIOĞLU, 2021) Yüksekkaya, Hazal; Pişkin, ErhanIn this paper, we consider a Kirchhoff-type viscoelastic equation with distributed delay and source terms. We obtain the nonexistence of global solutions under suitable conditions.Öğe Nonexistence of global solutions of a delayed wave equation with variable-exponents(Univ Miskolc Inst Math, 2021) Pişkin, Erhan; Yüksekkaya, HazalThis work deals with a Petrovsky equation with delay term and variable exponents. Firstly, we establish the local existence result by the Faedo-Galerkin method. Later, we prove the blow-up of solutions in a finite time. Our results are more general than the earlier results.Öğe Nonexistence of Solutions for a Logarithmic m-Laplacian Type Equation with Delay Term(Mehmet Zeki SARIKAYA, 2021) Yüksekkaya, Hazal; Pişkin, ErhanIn this work, we consider a logarithmic m-Laplacian type equation with delay term with initial and boundary conditions. Under suitable conditions on the initial data, we study the nonexistence of solutions in a finite time with negative initial energy $E\left( 0\right) <0$ in a bounded domain.Öğe Nonexistence of Solutions of a Delayed Wave Equation with Variable-Exponents(Murat TOSUN, 2020) Pişkin, Erhan; Yüksekkaya, HazalIn this paper, we deal with a nonlinear Timoshenko equation with delay term and variable exponents. Under suitable conditions, we prove the blow-up of solutions in a finite time. Our results are more general than the earlier results. Time delays arise in many applications, for instance, it appears in physical, chemical, biological, thermal and economic phenomena. Also, delay is source of instability, a small delay can destabilize a system which is uniformly asymptotically stable. 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 Nonexistence of solutions for a higher-oırder wave equation with delay and variable-exponents(Springer Science and Business Media Deutschland GmbH, 2022) Pişkin, Erhan; Yüksekkaya, HazalIn this article, we deal with a higher-order wave equation with delay term and variable exponents. Under suitable conditions, we prove the nonexistence of solutions in a finite time. Generally, the problems with variable exponents arise in many branches in sciences such as nonlinear elasticity theory, electrorheological fluids and image processing. Time delays often appear in many practical problems such as thermal, biological, chemical, physical and economic phenomena.Öğe Stability result for a kirchhoff beam equation with variable exponent and time delay(Emrah Evren KARA, 2022) Ferreira, Jorge; Pişkin, Erhan; Raposo, Carlos; Shahrouzi, Mohammad; Yüksekkaya, HazalThis paper is concerned with a stability result for a Kirchhoff beam equation with variable exponents and time delay. The exponential and polynomial stability results are proved based on Komornik’s inequality.Öğe Well-posedness and exponential stability for the logarithmic Lamé system with a time delay(Taylor and Francis Ltd., 2023) Yüksekkaya, Hazal; Pişkin, Erhan; Kafini, Mohammad M.; Al-Mahdi, Adel M.This paper is concerned with the initial-boundary value problem for a log-arithmic Lamé system with a time delay in a bounded domain. We provethe well-posedness of the system by utilizing the semigroup theory. Then,we prove the existence of global solutions by using the well-depth method.In addition, we establish an exponential stability decay result under appro-priate assumptions on the weight of the time delay and that of frictional damping.
