Yazar "Selçuk, Burhan" seçeneğine göre listele

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    Blow up for porous medium equations
    (2021) Selçuk, Burhan
    In various branches of applied sciences, porous medium equations exist where this basic model occurs in a natural fashion. It has been used to model fluid flow, chemical reactions, diffusion or heat transfer, population dynamics, etc.. Nonlinear diffusion equations involving the porous medium equations have also been extensively studied. However, there has not been much research effort in the parabolic problem for porous medium equations with two nonlinear boundary sources in the literature. This paper adresses the following porous medium equations with nonlinear boundary conditions. Firstly, we obtain finite time blow up on the boundary by using the maximum principle and blow up criteria and existence criteria by using steady state of the equation $k_{t}=k_{xx}^{n},(x,t)\\in (0,L)\\times (0,T)\\ $with $ k_{x}^{n}(0,t)=k^{\\alpha }(0,t)$, $k_{x}^{n}(L,t)=k^{\\beta }(L,t)$,$\\ t\\in (0,T)\\ $and initial function $k\\left( x,0\\right) =k_{0}\\left( x\\right) $,$\\ x\\in \\lbrack 0,L]\\ $where $n>1$, $\\alpha \\ $and $\\beta \\ $and positive constants.
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    The quenching behavior of a nonlinear parabolic equation with a singular boundary condition
    (2015) Özalp, Nuri; Selçuk, Burhan
    In this paper, we study the quenching behavior of solution of a nonlin- ear parabolic equation with a singular boundary condition. We prove finite-time quenching for the solution. Further, we show that quench- ing occurs on the boundary under certain conditions. Furthermore, we show that the time derivative blows up at quenching point. Also, we get a lower solution and an upper bound for quenching time. Finally, we get a quenching rate and lower bounds for quenching time.
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    The quenching behavior of a parabolic system
    (2013) Selçuk, Burhan
    In this paper, we study the quenching behavior of solution of aparabolic system. We prove …nite-time quenching for the solution. Further,we show that quenching occurs on the boundary under certain conditions.Furthermore, we show that the time derivative blows up at quenching time.Finally, we get a quenching criterion by using a comparison lemma and wealso get a quenching rate
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    Quenching behavior of a semilinear reaction-diffusion system with singularboundary condition
    (2016) Selçuk, Burhan
    In this paper, we study the quenching behavior of the solution of a semilinear reaction-diffusion system with singular boundary condition. We first get a local exisence result. Then we prove that the solution quenches only on the right boundary in finite time and the time derivative blows up at the quenching time under certain conditions. Finally, we get lower bounds and upper bounds for quenching time.
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    Quenching for a nonlinear diffusion equation with singular boundary outfluxes
    (2018) Selçuk, Burhan; Özalp, Nuri
    In this paper, we study a nonlinear diffusion equation (?(u))t = uxx, 0 < x < a, t > 0 with singularboundary outfluxes ux(0, t) = u?p(0, t), ux(a, t) = ?u?q(a, t). Firstly, we get the quenching occurs in a finite time atthe boundary x = a under certain conditions. Finally, we show the time derivative blows up at the quenching timeand we also establish results on quenching time and rate for certain nonlinearities.