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    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, Nazli
    In 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 term
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    Öğe
    LOCAL EXISTENCE AND BLOW UP FOR P-LAPLACIAN EQUATION WITH LOGARITHMIC NONLINEARITY
    (Univ Miskolc Inst Math, 2022) Irkil, Nazli; Piskin, E.
    This paper deals with a problem of a wave equation with p-Laplacian and logarithmic nonlinearity term. Firstly, local existence of weak solutions have been obtained by applying Banach fixed theorem. Later, the finite-time blow up of the solutions have been obtained for negative initial energy.
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    Öğe
    MATHEMATICAL BEHAVIOR OF SOLUTIONS OF P-LAPLACIAN EQUATION WITH LOGARITHMIC SOURCE TERM
    (Yildiz Technical Univ, 2019) Piskin, Erhan; Irkil, Nazli
    For the p-Laplacian wave equation with logarithmic nonlinearity of initial value problem is analyzed. Focusing on the interplay between damped term and logarithmic source, we discuss the local existence of solutions.
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    Öğe
    On the p-Laplacian type equation with logarithmic nonlinearity: Existence, decay and blow up
    (Univ Nis, Fac Sci Math, 2023) Irkil, Nazli
    This work is deal with a problem of wave equation with p-Laplacian, strong damping and logarithmic source terms under initial-boundary conditions. The global existence of weak solution was proved for related to the equation. Global existence results of solutions are obtained using the potential well method, Galerkin method and compactness approach corresponding to the logarithmic source term. Besides, we established the energy functional decaying polynomially to zero as the time goes to infinity due to Nakao's inequality and some precise priori estimates on logarithmic nonlinearity. For suitable conditions we proved the finite time blow up results of solutions. The proof is based on the concavity method, perturbation energy method and differential-integral inequality technique. Additionally, under suitable assumptions on initial data, the infinite time blow up result is investigated with negative initial energy.