A PRIORI BOUNDS OF STATIONARY SOLUTIONS OF TWO DIMENSIONAL KELLER-SEGEL SYSTEM ON POLYGONAL DOMAINS

Mimura Yoshifumi

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A PRIORI BOUNDS OF STATIONARY SOLUTIONS OF TWO DIMENSIONAL KELLER-SEGEL SYSTEM ON POLYGONAL DOMAINS

机译：多边形域上二维二维Keller-Segel系统的平稳解的先验界

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We consider a Neumann boundary problem like Ge Hand's problem on polygonal domains and prove that a priori bounds of solutions fail for specific parameters. The same results are already proved by Senba-Suzuki in 2000 when domains are open sets in R-2 with smooth boundaries. The novelty is that the foregoing specific parameters depend on angles of polygonal domains.

机译：我们考虑了像多边形区域上的葛汉德问题之类的诺伊曼边界问题，并证明对于特定参数，解的先验边界会失效。 Senba-Suzuki在2000年已经证明了相同的结果，当时域是R-2中具有光滑边界的开放集。新颖之处在于，前述特定参数取决于多边形域的角度。

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《Differential and integral equations》 |2015年第4期|共14页
作者
Mimura Yoshifumi;
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正文语种 eng
中图分类微分方程、积分方程;
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1. A PRIORI BOUNDS OF STATIONARY SOLUTIONS OF TWO DIMENSIONAL KELLER-SEGEL SYSTEM ON POLYGONAL DOMAINS [J] . Mimura Yoshifumi Differential and integral equations . 2015,第3a4期

机译：多边形域上二维二维Keller-Segel系统的平稳解的先验界
2. GLOBAL BOUNDED SOLUTIONS OF THE HIGHER-DIMENSIONAL KELLER-SEGEL SYSTEM UNDER SMALLNESS CONDITIONS IN OPTIMAL SPACES [J] . XLNRU CAO Discrete and continuous dynamical systems . 2015,第5期

机译：最优空间中小条件下高维KELLER-SEGEL系统的整体有界解
3. WEIGHTED A PRIORI ESTIMATES FOR THE SOLUTION OF THE DIRICHLET PROBLEM IN POLYGONAL DOMAINS IN R~2 [J] . Marcela Sanmartino, Marisa Toschi Real analysis exchange . 2014,第2期

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5. Normalized p-laplacian evolution: boundary behavior of non-negative solutions of fully nonlinear parabolic equations: Gradient bounds for p-harmonic systems with vanishing neumann (dirichlet) data in a convex domain. [D] . Banerjee, Agnid. 2014

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6. Functional Data Approximation on Bounded Domains using Polygonal Finite Elements [O] . Juan Cao, Yanyang Xiao, Zhonggui Chen, -1

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7. Global bounded solutions of the higher-dimensional Keller-Segel system under smallness conditions in optimal spaces [O] . Xinru Cao 2015

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8. Bounds for Solutions of a System of Linear Partial Differential Equations on Domains with Bergman-Silov Boundary [R] . Mitchell, J. 1964

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A PRIORI BOUNDS OF STATIONARY SOLUTIONS OF TWO DIMENSIONAL KELLER-SEGEL SYSTEM ON POLYGONAL DOMAINS

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