On the existence of kernel functions for the heat equation in n dimensions

dc.contributor.advisorJones, B. Franken_US
dc.creatorShapiro, Michael Richarden_US
dc.date.accessioned2018-12-18T21:29:25Zen_US
dc.date.available2018-12-18T21:29:25Zen_US
dc.date.issued1973en_US
dc.description.abstractLet be a bounded open set in Fnx (tQ,t^) such that each cross section t = nfl(Rnx {t}) is star-like. We define the lateral boundary ST Q = U SO,. L t€(t,tl) C and the parabolic boundary S^O = ô^O U t where fl. denotes the base of * c Theorem 1.1: Let be as above, then there exists a function u such that u is continuous in OU S^O* u > in Q, u = on S^O, and u is caloric in . Theorem 122; Suppose the boundary of extends continuously to a point (x',tQ) in the boundary of the base. Then there exists a kernel function in at the point (x',tQ). Theorem 1.3: There exists a kernel function at an interior point (XQ,tg) of the base of . If we restrict our attention somewhat we obtain the 2 following asymptotic relations Suppose a e c (,1], aa." e L^(,1), a(t) •> as t -* , and a > on (,T).en_US
dc.format.digitalOriginreformatted digitalen_US
dc.format.extent28 ppen_US
dc.identifier.callnoThesis Math. 1973 Shapiroen_US
dc.identifier.citationShapiro, Michael Richard. "On the existence of kernel functions for the heat equation in n dimensions." (1973) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/104723">https://hdl.handle.net/1911/104723</a>.en_US
dc.identifier.digitalRICE2359en_US
dc.identifier.urihttps://hdl.handle.net/1911/104723en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.titleOn the existence of kernel functions for the heat equation in n dimensionsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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