UNIFORM BLOWUP PROFILES FOR DIFFUSION EQUATIONS WITH NONLOCAL SOURCE AND NONLOCAL BOUNDARY1

作     者：LinZhigui LiuYurong Lin Zhigui Liu YurongSchool of Mathematical Science, Yangzhou University, Yangzhou 225002, China

作者机构：SchoolofMathematicalScienceYangzhouUniversityYangzhou225002China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2004年第24卷第3期

页      面：443-450页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：国家自然科学基金(10171088) SRF for Rocs, SEM 

主　　题：Blowup nonlocal source nonlocal boundary condition 35K50 35B40 

摘      要：Long time behavior of solutions to semilinear parabolic equations with nonlo-cal nonlinear source ut-Δu=∫Ωg(u)dx in Ω×(0, T) and with nonlocal boundary con-dition u(x, t)=∫Ωf(x, y)u(y,t)dy on эΩ×(0, T) is studied. The authors establish local existence, global existence and nonexistence of solutions and discuss the blowup properties of solutions. Moveover, they derive the uniform blowup estimates for g(s)= s^p(p1) and g(s)=e^э under the assumption ∫Ωf(x,y)dy1 for x∈эΩ.