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KOÇ UNIVERSITY
GRADUATE SCHOOL OF SCIENCES & ENGINEERING
MATHEMATICS
MS THESIS DEFENSE BY NİDA FİDAN
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Title: Blow up Solutions of Nonlinear Parabolic Equations
Speaker: Nida Fidan
Time: August 24, 2017, 14.00
Place: Eng 208
Koç University
Rumeli Feneri Yolu
Sariyer, Istanbul
Thesis Committee Members:
Prof. Varga Kalantarov (Advisor, Koc University)
Assoc. Prof. Mine Çağlar (Koc University)
Prof. Davut Uğurlu (Piri Reis University)
Abstract:
In this thesis, we study the problem of blow up solutions of second order nonlinear parabolic equations and numerical analysis of blow up solutions. Firstly, blow up solutions in semilinear heat equation is examined and three methods namely concavity method, eigenfunction method and comparison method are explained. Secondly, the finite difference approximation to the initial boundary value problem for semilinear heat equation is studied. Two convergence results are shown; the convergence of finite difference solution to the exact solution and the convergence of numerical blow up time to the exact blow up time.