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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 positive initial-energy solutions for coupled nonlinear wave equations with degenerate damping and source terms(Springeropen, 2015) Piskin, ErhanIn this work, we consider coupled nonlinear wave equations with degenerate damping and source terms. We will show the blow up of solutions in finite time with positive initial energy. This improves earlier results in the literature.Öğe BLOW UP OF POSITIVE INITIAL-ENERGY SOLUTIONS FOR THE EXTENSIBLE BEAM EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS(Univ Nis, 2016) Piskin, Erhan; Irkil, NazliIn this paper, we study the following extensible beam equation u(tt) + Delta(2)u - M (parallel to del u parallel to(2)) Delta u + vertical bar u(t)vertical bar(p-1) ut = vertical bar u vertical bar(q-1) u with initial and boundary conditions. Under suitable conditions on the initial datum, we prove that the solution blows up in finite time with positive initial -energy. Keywords: Extensible beam equation, blow up, nonlinear damping termÖğe 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 fourth-order reaction-diffusion equation in variable-exponent Sobolev spaces(Univ Nis, Fac Sci Math, 2024) Butakin, Gulistan; Piskin, ErhanThis work deals with a fourth order reaction-diffusion equation with variable exponents. Firstly, we investigate the finite time blow-up of solutions for positive initial energy. Later, we establish by utilizing a technique differential inequalities an upper limit on the blow-up time.Öğe BLOW UP OF SOLUTIONS FOR A PETROVSKY TYPE EQUATION WITH LOGARITHMIC NONLINEARITY(Korean Mathematical Soc, 2022) Ferreira, Jorge; Irkl, Nazl; Piskin, Erhan; Raposo, Carlos; Shahrouzi, MohammadThis paper aims to investigate the initial boundary value problem of the nonlinear viscoelastic Petrovsky type equation with nonlinear damping and logarithmic source term. We derive the blow-up results by the combination of the perturbation energy method, concavity method, and differential-integral inequality technique.Öğe BLOW UP OF SOLUTIONS FOR VISCOELASTIC WAVE EQUATIONS OF KIRCHHOFF TYPE WITH ARBITRARY POSITIVE INITIAL ENERGY(Texas State Univ, 2017) Piskin, Erhan; Fidan, AyseIn this article we consider the nonlinear Viscoelastic wave equations of Kirchh off type u(tt) - M(parallel to del u parallel to(2))Delta u + integral(t)(0) g(1)(t - tau)Delta u(tau)d tau + u(t) = (p + 1)vertical bar v vertical bar(q+1)vertical bar u vertical bar(p-1) u, u(tt) - M(parallel to del v parallel to(2))Delta v + integral(t)(0) g(2)(t - tau)Delta v(tau)d tau + v(t) = (q + 1)vertical bar u vertical bar(p+1)vertical bar v vertical bar(q-1) v, with initial conditions and Dirichlet boundary conditions. We proved the global nonexistence of solutions by applying a lemma by Levine, and the concavity method.Öğe BLOW UP SOLUTIONS FOR A CLASS OF NONLINEAR HIGHER-ORDER WAVE EQUATION WITH VARIABLE EXPONENTS(Yildiz Technical Univ, 2019) Piskin, ErhanIn this paper, we consider a class of nonlinear higher-order wave equation with variable exponents u(tt) + (-Delta)(m)u +vertical bar u(t)vertical bar(p(x)-2)u(t) = vertical bar u vertical bar(q(x)-2)u in a bounded domain Omega subset of R-n. We prove a finite time blow up result for the solutions with negative initial energy. This improves earlier results in the literature [18].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 BLOW-UP AND DECAY OF SOLUTIONS FOR A DELAYED TIMOSHENKO EQUATION WITH VARIABLE-EXPONENTS(Univ Miskolc Inst Math, 2022) Yueksekkaya, Hazal; Piskin, ErhanThis work deals with a Timoshenko equation with delay term and variable exponents. Firstly, we obtain the blow up of solutions for negative initial energy in a finite time. Later, we establish the decay results by using an integral inequality due to Komornik. These, improve and extend the previous studies in the literature.Öğe BLOW-UP OF SOLUTIONS FOR A LOGARITHMIC QUASILINEAR HYPERBOLIC EQUATION WITH DELAY TERM(Univ Prishtines, 2021) Piskin, Erhan; Yuksekkaya, 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 OF WEAK SOLUTIONS FOR A HIGHER-ORDER HEAT EQUATION WITH LOGARITHMIC NONLINEARITY(Univ Miskolc Inst Math, 2023) Comert, Tugrul; Piskin, ErhanThis paper deal with the initial boundary value problem for a higher-order heat equation with logarithmic source term ut + (-& UDelta;)mu -& UDelta;ut = uk-2u ln |u|. We obtain blow-up of weak solutions in the finite time, by employing potential well technique and concave technique. In addition, the upper bound of blow-up time is considered. This improves and extends some previous studies.Öğe Blowup and Global Solutions of a Fourth-Order Parabolic Equation With Variable Exponent Logarithmic Nonlinearity(Wiley, 2024) Butakin, Gulistan; Piskin, Erhan; Celik, ErcanIn this work, we deal with a fourth-order parabolic equation with variable exponent logarithmic nonlinearity. We obtain the global existence and blowup solutions using the energy functional and potential well method.Öğe Decay and blow up at infinite time of solutions for a logarithmic Petrovsky equation(Tbilisi Centre Math Sci, 2020) Piskin, Erhan; Calisir, ZeynepIn this work, we consider a logarithmic Petrovsky equation with strong damping with initial and boundary conditions in a bounded domain. Under suitable conditions, we prove decay of solutions. Also, we establish the blow up at infinite time of solutions.Öğe Decay rate and blow up solutions for coupled quasilinear system(Springer Int Publ Ag, 2020) Mezouar, Nadia; Piskin, ErhanWe consider the initial value problem for a coupled quasilinear system in a bounded domain with dispersion, nonlinear damping and source terms. We give decay estimate of energy function by means Nakao's inequality. Furthermore, under some conditions on the given parameters, we study blow up of solutions for a negative initial energy.Öğe Existence and asymptotic behavior for a logarithmic viscoelastic plate equation with distributed delay(Semnan Univ, 2022) Piskin, Erhan; Ferreira, Jorge; Yuksekkaya, Hazal; Shahrouzi, MohammadIn this article, we consider a logarithmic viscoelastic plate equation with distributed delay. Firstly, we study the local and global existence of solutions by using the energy method combined with Faedo-Galerkin method. Then, by introducing a suitable Lyapunov functional, we prove the asymptotic behavior of the solution. Our results are more general than the earlier results.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 FOR A STRONGLY DAMPED PETROVSKY EQUATION WITH VARIABLE-EXPONENT NONLINEARITIES(Texas State Univ, 2021) Antontsev, Stanislav; Ferreira, Jorge; Piskin, 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.
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