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Öğe Blow up and quenching for a problem with nonlinear boundary conditions(Texas State University - San Marcos, 2015) Ozalp, N.; Selcuk, B.In this article, we study the blow up behavior of the heat equation ut = uxx with ux(0, t) = up(0, t), up(0, t) = ux(a, t). We also study the quenching behavior of the nonlinear parabolic equation vt = vxx +2v2x =(1-v) with vx(0, t) = (1 - v(0, t))-p+2, vx(a, t) = (1 v(a; t))-q+2. In the blow up problem, if u0 is a lower solution then we get the blow up occurs in a finite time at the boundary x = a and using positive steady state we give criteria for blow up and non-blow up. In the quenching problem, we show that the only quenching point is x = a and vt blows up at the quenching time, under certain conditions and using positive steady state we give criteria for quenching and non-quenching. These analysis is based on the equivalence between the blow up and the quenching for these two equations. © 2015 Texas State University - San Marcos.Öğe The quenching behavior of a nonlinear parabolic equation with a singular boundary condition(Hacettepe University, 2015) Ozalp, N.; Selcuk, B.In this paper, we study the quenching behavior of solution of a nonlinear parabolic equation with a singular boundary condition. We prove finite-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 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. © 2015, Hacettepe Journal of Mathematics and Statistics. All rights reserved.Öğe The quenching behavior of a semilinear heat equation with a singular boundary outflux(American Mathematical Society, 2014) Selcuk, B.; Ozalp, N.In this paper, we study the quenching behavior of the solution of a semilinear heat equation with a singular boundary outflux. We prove a finite-time quenching for the solution. Further, we show that quenching occurs on the boundary under certain conditions and we show that the time derivative blows up at a quenching point. Finally, we get a quenching rate and a lower bound for the quenching time. © 2014 Brown University.Öğe Quenching behavior of semilinear heat equations with singular boundary conditions(Texas State University - San Marcos, 2015) Selcuk, B.; Ozalp, N.In this article, we study the quenching behavior of solution to the semilinear heat equation (Formula presented) with f(v) = u-r or (1 – v)–r and (Formula presented) For this, we utilize the quenching problem ut=uxx with ux(0,t)=u-p(0,t), ux(a,t)=(1-u(a,t))-q. In the second problem, if u0 is an upper solution (a lower solution) then we show that quenching occurs in a finite time, the only quenching point is x=0 (x=a) and utblows up at quenching time. Further, we obtain a local solution by using positive steady state. In the first problem, we first obtain a local solution by using monotone iterations. Finally, for f(v)=-v-r ((1-v)-r), if v0 is an upper solution (a lower solution) then we show that quenching occurs in a finite time, the only quenching point is x=0 (x=a) and vt blows up at quenching time. © 2015 Texas State University.Öğe QUENCHING FOR A REACTION-DIFFUSION EQUATION WITH WEAK SINGULARITIES(Turkic World Mathematical Soc, 2022) Selcuk, B.This paper studies the following reaction-diffusion equation with a weak singular boundary condition. The primary objective for this problem is to analyze the quenching properties. It is obtained that finite time quenching occurs on the left bound-ary, the time derivative of the solution blows up at the same time and also quench-ing rate estimates of the solution of the eqaution kt(x, t) = kxx(x, t) + ln alpha k(x, t), (x, t) is an element of (0, 1) x (0, T) with kx (0, t) = - ln beta k(0, t), kx (1, t) = 0, t is an element of (0, T) and ini-tial function k (x, 0) = k0 (x) with [0, 1] -> (0, 1) where 0 < alpha, beta < 1 and T is a finite time.Öğe QUENCHING FOR A REACTION-DIFFUSION EQUATION WITH WEAK SINGULARITIES(Isik University, 2022) Selcuk, B.Abstract. This paper studies the following reaction-diffusion equation with a weak singular boundary condition. The primary objective for this problem is to analyze the quenching properties. It is obtained that finite time quenching occurs on the left boundary, the time derivative of the solution blows up at the same time and also quenching rate estimates of the solution of the eqaution (Formula Presented) and (Formula Presented) and T is a finite time. © Isk University, Department of Mathematics, 2022; all rights reserved.Öğe Splint efficacy in chronic post-stroke spasticity: a pilot study(University School of Physical Education in Wroclaw, 2022) Onder, B.; Selcuk, B.; Atci, A.G.; Kurtaran, A.; Akyuz, M.Introduction. Hand spasticity after stroke is a serious issue and may lead to hygiene problems, range of motion limitations, or contractures. Hand splints are often used to reduce spasticity and prevent movement limitations; however, there is little research available on the efficacy of splints in spasticity. The study aimed to investigate the efficacy of a reflex inhibitory splint (RiS) for upper extremity spasticity in stroke patients by using clinical and electrophysiological studies. Methods. Stroke patients with elbow and hand spasticity were allocated into 2 groups. The splint group (n = 16) wore RiS. The control group (n = 13) did not wear any upper extremity splint. Both groups received the same rehabilitation program during this period. They were evaluated for motion in the upper extremity with the Brunnstrom scale and Fugl-Meyer upper extremity scale. Electrophysiological measurements showing motor neuron excitability such as the ratio between the maximum amplitude of H-reflex and the maximum amplitude of M-response (Hmax/Mmax ratio), H-reflex latency, and F-wave persistence and latency were also studied. All clinical and electrophysiological measurements were performed in both groups on days 0 and 15. Results. At the end of the treatment, elbow and finger flexion tonus decreased and active wrist extension angle increased in the splint treatment group compared with both baseline and the control group. Compared with the pre-treatment status, a correlation was detected between the Hmax/Mmax ratio and the wrist flexion tonus in the splint group. Conclusions. RiS may be useful for the management of post-stroke upper-limb spasticity. © Wroclaw University of Health and Sport SciencesÖğe Topology properties of hierarchical honeycomb meshes(CEUR-WS, 2021) Selcuk, B.; Tankul, A.N.A.; Karci, A.Honeycomb meshes can be seen widely in nature and are using in many different areas because of its properties. Using honeycomb meshes for constructing hierarchical structures has some advantages. In this study, hierarchical honeycomb meshes (HHM) are investigated. The construction of HHM is introduced with an example, topological properties of HHM explained in detail, a labeling algorithm in the process of the construction phase and also routing algorithms are given. This study shows a HHM(n) has a fractal structure and its graph is a Hamiltonian graph. © 2021 Copyright for this paper by its authors.
