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  • 标题:Boundary control of a singular reaction-diffusion equation on a disk
  • 本地全文:下载
  • 作者:Rafael Vazquez ; Miroslav Krstic
  • 期刊名称:IFAC PapersOnLine
  • 印刷版ISSN:2405-8963
  • 出版年度:2016
  • 卷号:49
  • 期号:8
  • 页码:74-79
  • DOI:10.1016/j.ifacol.2016.07.421
  • 语种:English
  • 出版社:Elsevier
  • 摘要:AbstractRecently, the problem of boundary stabilization for unstable linear constant-coefficient reaction-diffusion equation on n-balls (in particular, disks and spheres) has been solved by means of the backstepping method. However, the extension of this result to spatially-varying coefficients is far from trivial. As a first step, this work deals with radially-varying reaction coefficients under revolution symmetry conditions on a disk (the 2-D case). Under these conditions, the equations become singular in the radius. When applying the backstepping method, the same type of singularity appears in the backstepping kernel equations. Traditionally, well-posedness of the kernel equations is proved by transforming them into integral equations and then applying the method of successive approximations. In this case, the resulting integral equation is singular. A successive approximation series can still be formulated, however its convergence is challenging to show due to the singularities. The problem is solved by a rather non-standard proof that uses the properties of the Catalan numbers, a well-known sequence frequently appearing in combinatorial mathematics.
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