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dc.contributor.authorKeady, Grant
dc.contributor.authorWiwatanapataphee, Benchawan
dc.date.accessioned2020-05-18T03:10:58Z
dc.date.available2020-05-18T03:10:58Z
dc.identifier.citationKeady, G. and Wiwatanapataphee, B. Functions with constant Laplacian satisfying Robin boundary conditions on an ellipse.
dc.identifier.urihttp://hdl.handle.net/20.500.11937/79264
dc.description.abstract

We study the problem of finding functions, defined within and on an ellipse, whose Laplacian is -1 and which satisfy a homogeneous Robin boundary condition on the ellipse. The parameter in the Robin condition is denoted by beta. The general solution and various asymptotic approximations are obtained. To find the general solution, the boundary value problem is formulated in elliptic cylindrical coordinates. A Fourier series solution is then derived. The Fourier coefficients satisfy a 3-term recurrence relation which can be solved. The integral of the solution over the ellipse, denoted by Q, is a quantity of interest in some physical applications. The dependence of Q on beta and the ellipse geometry is found. Finding asymptotics directly from the pde formulations is easier than from our series solution. We use the asymptotic approximations to Q as checks on the series solution. Several other inequalities are also used to check the solution. It is intended that this arXiv preprint will be referenced by the journal version, which will be submitted soon, as the arXiv contains material, e.g. codes for calculating Q, not in the much shorter journal version. Maple codes used in deriving or checking results in this paper are in the process of being tidied prior to being made available via links given at the URL given in the pdf version.

dc.subjectmath.AP
dc.subjectmath.AP
dc.subject35J05
dc.titleFunctions with constant Laplacian satisfying Robin boundary conditions on an ellipse
dc.typeJournal Article
dc.date.updated2020-05-18T03:10:58Z
curtin.departmentEngineering Support Services
curtin.departmentSchool of Electrical Engineering, Computing and Mathematical Sciences (EECMS)
curtin.accessStatusFulltext not available
curtin.facultyFaculty of Science and Engineering
curtin.contributor.orcidWiwatanapataphee, Benchawan [0000-0003-1875-6984]
curtin.contributor.orcidKeady, Grant [0000-0001-9413-2968]
curtin.contributor.researcheridWiwatanapataphee, Benchawan [E-5421-2010]
curtin.contributor.scopusauthoridWiwatanapataphee, Benchawan [6508175775]


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