擬線性拋物型方程之非線性邊界值問題的自我相似解
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2006
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這篇論文主要是研究擬線性拋物型方程之非線性邊界值問題的自我相似解。首先，我們證明了解的消失性。然後，藉研究所對應之常微分方程的初值問題，我們利用投射法證明了單調遞減全域解的存在。最後，我們分析任一單調遞減全域解的漸近行為。
In this paper, we study the self-similar solutions for a quasilinear parabolic equation with nonlinear boundary condition. We first prove that quenching always occurs. Then, by considering the initial value problem, we prove the existence of globally monotone decreasing solutions by a shooting method. Finally, we study the asymptotic behavior of any globally monotone decreasing solution.
In this paper, we study the self-similar solutions for a quasilinear parabolic equation with nonlinear boundary condition. We first prove that quenching always occurs. Then, by considering the initial value problem, we prove the existence of globally monotone decreasing solutions by a shooting method. Finally, we study the asymptotic behavior of any globally monotone decreasing solution.
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擬線性拋物型方程, 自我相似解, 消失性, 投射法, 漸近行為, quasilinear parabolic equation, self-similar solutions, quenching, shooting method, asymptotic behavior