Yazar "Ferreira, Jorge" seçeneğine göre listele

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    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, Mohammad
    This 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.
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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 asymptotic behavior of beam-equation solutions with strong damping and p(x)-biharmonic operator
    (B.Verkin Institute for Low Temperature Physics and Engineering of the NAS of Ukraine, 2022) Ferreira, Jorge; Panni, Willian S.; Messaoudi, Salim A.; Pişkin, Erhan; Shahrouzi, Mohammad
    In this paper, we consider a nonlinear beam equation with a strong damping and the p(x)-biharmonic operator. The exponent p(·) of nonlinearity is a given function satisfying some condition to be specified. Applying Faedo– Galerkin’s method, the existence of weak solutions is proved. Using Nakao’s lemma, the asymptotic behavior of weak solutions is established with mild assumptions on the variable exponent p(·). We show the asymptotic behavior of the weak solution is exponentially and algebraically depending on the variable exponent. This work improves and extends many other results in the literature.
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    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, Erhan
    In 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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    Existence and blow up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities
    (Texas State University, 2021) Antontsev, Stanislav; Ferreira, Jorge; Pişkin, Erhan
    In 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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    Existence and non-existence of solutions for Timoshenko-type equations with variable exponents
    (Pergamon-Elsevier Science Ltd, 2021) Antontsev, Stanislav N.; Ferreira, Jorge; Piskin, Erhan; Siqueira Cordeiro, Sebastiao Martins
    In this work, we investigate the following nonlinear Timoshenko variable exponents: u(tt) + Delta(2)u - M (parallel to del u parallel to(2)(L2(Omega))) Delta u + vertical bar u(t)vertical bar(p(x)-2) u(t) = vertical bar u vertical bar(q(x)-2)u. By using the Faedo-Galerkin method, we prove the local existence of the solution under suitable conditions. We also investigate the nonexistence of solutions with negative initial energy. Published by Elsevier Ltd.
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    EXISTENCE OF GLOBAL WEAK SOLUTIONS FOR A p-LAPLACIAN INEQUALITY WITH STRONG DISSIPATION IN NONCYLINDRICAL DOMAINS
    (Texas State Univ, 2022) Ferreira, Jorge; Piskin, Erhan; Shahrouzi, Mohammad; Cordeiro, Sebastiao; Raposo, Carlos Alberto
    In this work, we obtain global solutions for nonlinear inequalities of p -Laplacian type in noncylindrical domains, for the unilateral problem with strong dissipation u '' - delta(pu) - delta u ' -f >= 0 in Q(0), where delta(p) is the nonlinear p -Laplacian operator with 2 <= p < infinity, and Q(0) is the noncylindrical domain. Our proof is based on a penalty argument by J. L. Lions and Faedo-Galerkin approximations.
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    General decay and blow up of solutions for a plate viscoelastic p(x)-Kirchhoff type equation with variable exponent nonlinearities and boundary feedback
    (Taylor & Francis Ltd, 2023) Ferreira, Jorge; Piskin, Erhan; Shahrouzi, Mohammad
    In this paper, we consider a plate viscoelastic p(x)-Kirchhoff type equation with variable-exponent nonlinearities of the formutt+ triangle(2)u(a+b integral(ohm)1/p(x)j del uj(p(x))dx)triangle(p(x))u integral(t)(0)g(ts)triangle(2)u(s)ds+beta triangle(2)ut+jutj(m(x)2)ut=juj(q(x)2)u,associated with initial and boundary feedback. Under appropriate conditions on p(.), m(.) and q(.), general decay result along the solution energy is proved. By introducing a suitable auxiliary function, it is also shown that regarding negative initial energy and a suitable range of variable exponents, solutions blow up in a finite time.
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    General decay and blow up of solutions for a plate viscoelastic p(x)-Kirchhoff type equation with variable exponent nonlinearities and boundary feedback
    (Taylor and Francis Ltd., 2024) Ferreira, Jorge; Pişkin, Erhan; Shahrouzi, Mohammad
    In this paper, we consider a plate viscoelastic p(x)–Kirchhoff type equation with variable-exponent nonlinearities of the form (Figure presented.) associated with initial and boundary feedback. Under appropriate conditions on p(·), m(·) and q(·), general decay result along the solution energy is proved. By introducing a suitable auxiliary function, it is also shown that regarding negative initial energy and a suitable range of variable exponents, solutions blow up in a finite time.
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    On the behavior of solutions for a class of nonlinear viscoelastic fourth-order p(x)-laplacian equation
    (Birkhauser, 2023) Shahrouzi, Mohammad; Ferreira, Jorge; Pişkin, Erhan; Zennir, Khaled
    In this work, we study the behavior of solutions for a class of nonlinear viscoelastic fourth-order p(x)-Laplacian equation with nonlinear boundary conditions. Under appropriate conditions on data, global existence of solutions, general decay and blow-up results with positive initial energy as well as negative have been proved.
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    Rao–Nakra sandwich beam with second sound
    (Elsevier B.V., 2021) Raposo, Carlos Alberto; Ferreira, Jorge; Pişkin, Erhan; Villagrán, Octavio Paulo Vera
    In this manuscript, we prove the well-posedness and exponential stability for a thermoelastic structure given by a Rao–Nakra sandwich beam. The system consists of two wave equations for the longitudinal displacements of the top and bottom layers, and one Euler–Bernoulli beam equation for the transversal displacement, where, the thermal disturbances are modeled by the propagation of wave-like pulses traveling at a finite speed, that is, we remove the physical paradox of infinite propagation speed in the classical theory of thermoelasticity within Fourier's law by using Cattaneo's law for heat conduction.
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    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, Hazal
    This 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.
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    Stability result for a variable-exponent viscoelastic double-Kirchhoff type inverse source problem with nonlocal degenerate damping term
    (Springer-Verlag Italia Srl, 2022) Shahrouzi, Mohammad; Ferreira, Jorge; Piskin, Erhan
    This paper aims to study the stability of solutions for a double-Kirchhoff type viscoelastic inverse source problem with nonlocal degenerate damping term and variable-exponent nonlinearities. Proving of existence and stability of solutions to inverse problems is of high importance because inverse problems are nonlinear and improperly posed, and the presence of unknown source functions with nonstandard growth conditions causes the nonexistence and blow-up of solutions. Therefore, in this work by using the suitable auxiliary functionals and by introducing a suitable Lyapunov functional, we shall prove that the solutions of a double-Kirchhoff type viscoelastic inverse source problem are asymptotically stable in the appropriate range of variable exponents.
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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.