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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 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 Existence and blow up of solutions for m ( x )- biharmonic equation with variable exponent sources(Univ Nis, Fac Sci Math, 2024) Butakin, Gulistan; Pis, ErhanIn this work concerned with the existence and blow up of solutions for m (x) - biharmonic equation with variable exponent sources. Under appropriate conditions, we discuss the stationary problem and potential wells. By using the Faedo-Galerkin method, we prove the global existence of the solution. We also investigate the blow up of solutions with negative initial energy.
