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Grow-up on the boundary for a semilinear parabolic problem. (English) Zbl 1090.35034

Chipot, Michel (ed.) et al., Nonlinear elliptic and parabolic problems. A special tribute to the work of Herbert Amann, Zürich, Switzerland, June 28–30, 2004. Basel: Birkhäuser (ISBN 3-7643-7266-4/hbk). Progress in Nonlinear Differential Equations and their Applications 64, 137-150 (2005).
The authors consider the problem \[ \begin{alignedat}{2} u_t&= u_{xx}- pu^{2p-1},\quad &0&< x< 1,\;t>0,\\ -u_x&= u^p, &x&= 0,\\ u_x&= 0, &x&=1,\\ u|_{t=0}&= u_0(x)\geq 0, &0&\leq x\leq 1, \end{alignedat} \] where \(p> 1\). They study the growth rate of these global unbounded solutions as \(t\to\infty\). The authors find their growth rate at the singular point on the boundary.
For the entire collection see [Zbl 1077.00009].

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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