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The asymptotic self-similar behavior for the quasilinear heat equation with nonlinear boundary condition |
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| Authors: | Zhiwen Duan |
| Affiliation: | aDepartment of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, PR China |
| Abstract: | In this paper the quasilinear heat equation with the nonlinear boundary condition is studied. The blow-up rate and existence of a self-similar solution are obtained. It is proved that the rescaled function v(y,t)=(T−t)1/(2p+α−2)u((T−t)(p−1)/(2p+α−2)y,t), | behaves as t→T like a nontrivial self-similar profile.
| Keywords: | Quasilinear heat equation Nonlinear boundary condition Lyapunov function Asymptotic self-similar behavior |
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