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Asymptotic behavior of solutions for a parabolic equation with nonlinear boundary conditions

Author: C. V. Pao
Journal: Proc. Amer. Math. Soc. 80 (1980), 587-593
MSC: Primary 35K60; Secondary 35B40
MathSciNet review: 587933
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Abstract: This paper is concerned with the asymptotic behavior and nonexistence of global solutions for a linear parabolic equation under nonlinear boundary conditions. It is shown under certain conditions on the nonlinear boundary function that a global solution exists and converges to a steady-state solution while for another class of initial function the solution blows-up in finite time. In some special cases, threshold results for the convergence of the solution and its blowingup behavior are explicitly given.

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Keywords: Asymptotic stability, nonexistence of global solutions, parabolic equations, nonlinear boundary conditions, upper and lower solutions
Article copyright: © Copyright 1980 American Mathematical Society

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