A note on well-posedness of semilinear reaction–diffusion problem with singular initial data
A note on well-posedness of semilinear reaction–diffusion problem with singular initial data
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关于奇异初始数据半线性反应扩散问题适定性的注解
DOI：
10.1016/j.jmaa.2011.06.023
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发表时间：
2011
影响因子：
1.3
通讯作者：
Mikolaj Sier.zkega
中科院分区：
文献类型：
--
作者：
James C. Robinson;Mikolaj Sier.zkega
讨论了具有Dirichlet边界条件的标量反应扩散方程ut = Δ u+ f（u）在初值无界时的适定性条件.标准增长条件与保证相关常微分方程u stec = f（u）的全局解的无爆破条件<$1 ∞ 1/f（s）ds =∞并列。在此条件下，我们研究了玩具偏微分方程ut = f（u）在Lp中的适定性.给出了一个例子，当反应扩散方程在L2（0，1）中整体适定时，源项f和初始条件ε ∈ L2（0，1）使得ε 1∞ 1/f（s）ds =∞，玩具偏微分方程瞬间爆破.
We discuss conditions for well-posedness of the scalar reaction–diffusion equation u t= Δ u+ f (u) equipped with Dirichlet boundary conditions where the initial data is unbounded. Standard growth conditions are juxtaposed with the no-blow-up condition∫ 1∞ 1/f (s) d s=∞ that guarantees global solutions for the related ODE u˙= f (u). We investigate well-posedness of the toy PDE u t= f (u) in L p under this no-blow-up condition. An example is given of a source term f and an initial condition ψ∈ L 2 (0, 1) such that∫ 1∞ 1/f (s) d s=∞ and the toy PDE blows-up instantaneously while the reaction–diffusion equation is globally well-posed in L 2 (0, 1).
影响因子：
1.1
作者：
M. Fila;H. Ninomiya;J. Vázquez
通讯作者：
M. Fila;H. Ninomiya;J. Vázquez