Local and global existence of solutions to a quasilinear degenerate chemotaxis system with unbounded initial data

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• 作者：Tomomi Yokota and Noriaki Yoshino
• 刊名：Mathematical Methods in the Applied Sciences
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：39
• 期：12
• 页码：3361-3380
• 全文大小：365K
• ISSN：1099-1476

文摘

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Marinoschi (J. Math. Anal. Appl. 2013; 402:415–439) established an abstract approach using nonlinear m-accretive operators to giving existence of local solutions to this system when 0 < D₀≤D′(r)≤D_∞<∞ and (r₁,r₂)↦K(r₁,r₂)r₁ is Lipschitz continuous on aces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">R2, provided that the initial data is assumed to be small. The smallness assumption on the initial data was recently removed (J. Math. Anal. Appl. 2014; 419:756–774). However the case of non-Lipschitz and degenerate diffusion, such as D(r) = r^m(m > 1), is left incomplete. This paper presents the local and global solvability of the system with non-Lipschitz and degenerate diffusion by applying (J. Math. Anal. Appl. 2013; 402:415–439) and (J. Math. Anal. Appl. 2014; 419:756–774) to an approximate system. In particular, the result in the present paper does not require any properties of boundedness, smoothness and radial symmetry of initial data. This makes it difficult to deal with nonlinearity. Copyright