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

查看全文 作　　者：LinZhigui [1]LiuYurong 机构地区：[1]SchoolofMathematicalScience,YangzhouUniversity,Yangzhou225002,China 出　　处：《Acta Mathematica Scientia》索引2004年第24卷第3期,共8页 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(p>1) and g(s)=e^э under the assumption ∫Ωf(x,y)dy<1 for x∈эΩ. 关 键 词：放大 标准线性偏微分方程 非线性 连续函数 均匀条件