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Stable Manifold Approximation for the Heat Equation with Nonlinear Boundary Condition

✍ Scribed by Gabriel Acosta; Julián Fernández Bonder; Julio D. Rossi


Book ID
111561630
Publisher
Springer US
Year
2000
Tongue
English
Weight
209 KB
Volume
12
Category
Article
ISSN
1040-7294

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The asymptotic self-similar behavior for
✍ Zhiwen Duan 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 877 KB

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) = (Tt) 1/(2p+α-2) u((Tt) (p-1)/(2p+α-2) y, t), behaves as t → T like a nontrivial self