Abstract: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 gi… Show more
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