方钟波,张舰匀

• 1:中国海洋大学数学科学学院

摘要(Abstract)：

研究具有加权非线性非局部边界条件的非局部热方程初边值问题中非负解的整体存在和爆破性质。利用上下解的方法找到了边界上的加权函数及非线性指数对解的整体存在性与爆破的影响。

关键词(KeyWords)： 热方程;权函数;整体存在;爆破

Abstract:

Keywords:

基金项目(Foundation): 山东省自然科学基金项目(ZR2012AM018);; 中央高校基本科研基金项目(201362032)资助

作者(Author): 方钟波,张舰匀

DOI: 10.16441/j.cnki.hdxb.2014.02.018

参考文献(References)：

• [1]Bebernes J,Eberly D.Mathematical Problems from Combustion Theory[M].New York:Springer-Verlag,1989.
• [2]Pao C V.Nonlinear Parabolic and Elliptic Equations[M].New York:Plenum Press,1992.
• [3]Day W A.Extensions of property of heat equation to linear thermoelasticity and other theories[J].Quart App1 Math,1982,40:319-330.
• [4]Day W A.A decreasing property of solutions of parabolic equations with applications to Thermoelasticity[J].Quart App1 Math,1983,40:468-475.
• [5]Deng K,Levine H A.The role of critical exponents in blow-up theorems:The sequel[J].J Math Anal Appl,2000,243:85-126.
• [6]Souplet P.Blow-up in nonlocal reaction-diffusion equations[J].SIAM J Math Anal,1998,29(6):1301-1334.
• [7]Niculescu C P,Roventa L.Generalized convexity and the existence of finite time blow-up solutions for an evolutionary problem[J].Nonl Anal,2012,75(1):270-277.
• [8]Friedman A.Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions[J].Quart Appl Math,1986,44(3):401-407.
• [9]Pao C V.Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions[J].J Comput Appl Math,1998,88(1):225-238.
• [10]Liu D M,Mu C L.Blow-up properties for a semilinear reactiondiffusion system with nonlinear nonlocal boundary conditions[J].Abstr Appl Anal,2010,Article ID 148035.
• [11]Cui Z J,Yang Z D.Roles of weight functions to a nonlinear porous medium equation with nonlocal source and nonlocal boundary condition[J].J Math Anal Appl,2008,342:559-570.
• [12]Gladkov A l,Kim K L.Blow-up of solutions for semilinear heat equation with nonlinear nonlocal boundary condition[J].J Math Appl,2008,338:264-273.
• [13]Wang Y L,Mu C L,Xiang Z Y.Properties of positive solution for nonlocal reaction diffusion equation with nonlocal boundary[J].Bound Value Pro,2007,Article ID64579.
• [14]Mu C L,Liu D M,Zhou S M.Properties of positive solutions for a nonlocal reaction-diffusion equation with nonlocal nonlinear boundary conditions[J].J Korean Math Soc,2010,47(6):317-1328.
• [15]Yin Y F.On nonlinear parabolic equations with nonlocal boundary condition[J].J Math Anal Appl,1994,185:5-60.

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