帶有反位勢(shì)函數(shù)的半線性熱方程解的性質(zhì).pdf

1、重慶大學(xué)碩士學(xué)位論文帶有反位勢(shì)函數(shù)的半線性熱方程解的性質(zhì)姓名：馮志敏申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：穆春來(lái)2010-04重慶大學(xué)碩士學(xué)位論文 英文摘要 II ABSTRACT The blow- up theory of the solutions for nonlinear evolution equations is an important aspect of partial differential equ

2、ation. In Chapter 2, we consider the properties of solitions for a semilinear heat equation ( ) ( ) pt u u V x u a x u = ? ? + for ( , ) (0, ) x t ∈?× ∞with nonlinear and nonlocal boundary condition ( )

3、 ( , ) , ( , ) l u x t K x y u y t dy? = ∫on (0, ) ?× ∞ . The conditions on the existence and nonexistence of global solutions are given by utilizing the method of subsolution and supersolution. In Ch

4、apter 3, we study the property of the equation with a gradient term and potential. We obtain the conditions for existence of solution by utilizing the regularity theory of parabolic equations