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Blowup of Solutions of Two Classes of Nonlinear Evolution Equations

Author: FanPing
Tutor: LiGang
School: Nanjing University of Information Engineering
Course: Applied Mathematics
Keywords: Semi- linear parabolic equations Nonlinear boundary conditions Blow up Rate Upper and lower bounds Blasting set
CLC: O175.2
Type: Master's thesis
Year: 2007
Downloads: 40
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Abstract


This paper mainly consider two types of nonlinear evolution equations solution blasting rate estimates and blasting set . The text consists of three parts: The first chapter is the introduction , introduces some basic background research progress , prior knowledge and articles used in the main principles and methods . The second chapter consider semilinear coupled parabolic equations where : p, q, m is the normal number , the B R = { x | | x | ≤ R , x ∈ R N }, η is ( ? ) outside the normal vector on the B R . Initial Value u 0 ( X ) , of V 0 ( x ) is radially symmetric, bounded continuous function nonnegative the V r < / sub > = ( ? ) v / ( ? ) r ≥ 0 , where r = | x | , and the compatibility conditions are satisfied : (?) u 0 / (?) η = v 0 p , (?) v 0 / (?) η = u 0 q . The rate of this chapter by using Scaling zoom principle , the nature of the Green function , as well as some complex calculations , has been the explosion cracked estimate also gives the nonlinear reaction term and absorption blasting rate . In the second chapter of the issues discussed on the basis of , Chapter III v equation t < / sub > = . Change the △ v v t = △ vu n < / sup > to fully understand the impact of different reaction term burst crack through similar methods , the available solutions blasting rate , the third chapter in the content analysis than the second chapter of complex many ; under certain conditions at the same time , the article by commonly used techniques method of undetermined coefficients and upper and lower solution method and comparison principle given blasting set of solutions .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations
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