Complete classification of shape functions of self-similar solutions |
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Authors: | Zhong Bo Fang Minkyu Kwak |
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Affiliation: | aDepartment of Mathematics, Chonnam National University, Kwangju 500-757, Republic of Korea |
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Abstract: | In this paper we study some asymptotic profiles of shape functions of self-similar solutions to the initial-boundary value problem with Neumann boundary condition for the generalized KPZ equation: ut=uxx−|ux|q, where q is positive number. The shapes of solutions of the corresponding nonlinear ordinary differential equation are of very different nature. The properties depend on the critical value and initial data as usual. |
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Keywords: | Self-similar solution Very singular solution Blow-up |
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