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Boundedness of global solutions for the heat equation with nonlinear boundary conditions. (English) Zbl 0702.35141
The heat equation with a nonlinear boundary condition is considered. The blow up phenomenon may occur for this problem, since the boundary condition describes an absorption law. It is shown in the paper that global solutions are uniformly bounded.
Reviewer: Marek Fila

MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35K05 Heat equation
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