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

Pao, C. V.

doi:10.1090/S0002-9939-1980-0587933-8

Asymptotic behavior of solutions for a parabolic equation with nonlinear boundary conditions
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Proc. Amer. Math. Soc. 80 (1980), 587-593 Request permission

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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