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    BLOW-UP OF SOLUTIONS FOR A LOGARITHMIC QUASILINEAR HYPERBOLIC EQUATION WITH DELAY TERM
    (Univ Prishtines, 2021) Piskin, Erhan; Yuksekkaya, Hazal
    In 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.
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    Existence and asymptotic behavior for a logarithmic viscoelastic plate equation with distributed delay
    (Semnan Univ, 2022) Piskin, Erhan; Ferreira, Jorge; Yuksekkaya, Hazal; Shahrouzi, Mohammad
    In 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.
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    EXISTENCE AND EXPONENTIAL DECAY OF A LOGARITHMIC WAVE EQUATION WITH DISTRIBUTED DELAY
    (Univ Miskolc Inst Math, 2023) Yuksekkaya, Hazal; Piskin, Erhan
    In this article, we deal with a logarithmic wave equation with distributed delay. Firstly, we establish the well-posedness 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 distributed delay and that of strong damping, we get the exponential decay results.
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    Local existence and blow up of solutions for a logarithmic nonlinear viscoelastic wave equation with delay
    (Univ Tabriz, 2021) Piskin, Erhan; Yuksekkaya, Hazal
    In this work, we consider a logarithmic nonlinear viscoelastic wave equation with a delay term in a bounded domain. We obtain the local existence of the solution by using the Faedo-Galerkin approximation. Then, under suitable conditions, we prove the blow up of solutions in finite time.
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    Mathematical behavior of solutions for a logarithmic p-Laplacian equation with distributed delay
    (Tbilisi Centre Math Sci, 2022) Piskin, Erhan; Yuksekkaya, Hazal
    In this article, we concerned with a logarithmic p-Laplacian equation with distributed internal delay. Firstly, we obtain the global existence of solutions by utilizing the well-depth method. Later, under appropriate assumptions on the weight of the delay and that of frictional damping, we establish the exponential decay. Moreover, we obtain the blow up results for negative initial energy.
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    Qualitative analysis of solutions for a class of logarithmic Kirchhoff equation with distributed delay
    (Tbilisi Centre Math Sci, 2022) Piskin, Erhan; Yuksekkaya, Hazal
    In this article, we concerned with a logarithmic Kirchhoff equation with distributed internal delay. Firstly, we obtain the global existence of solutions by using the well-depth method. Later, under appropriate assumptions on the weight of the delay and that of frictional damping, we establish the exponential decay. Moreover, we obtain the blow up results for negative initial energy.
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    A viscoelastic wave equation with delay and variable exponents: existence and nonexistence
    (Springer Int Publ Ag, 2022) Yuksekkaya, Hazal; Piskin, Erhan; Ferreira, Jorge; Shahrouzi, Mohammad
    This article deals with the existence and nonexistence of solutions for a viscoelastic wave equation with time delay and variable exponents on the damping and on source term. Firstly, we get the existence of weak solutions by combining the Banach contraction mapping principle and the Faedo-Galerkin method under suitable assumptions on the variable exponents m (.) and p (.). For nonincreasing positive function g, we obtain the nonexistence of solutions with negative initial energy in appropriate conditions.