Mathematics MS Thesis Defense by Nida Fidan

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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.