dc.contributor.advisor Jones, B. Frank Shapiro, Michael Richard 2018-12-18T21:29:25Z 2018-12-18T21:29:25Z 1973 https://hdl.handle.net/1911/104723 Let 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). 28 pp eng On the existence of kernel functions for the heat equation in n dimensions RICE2359 Thesis Text Mathematical Sciences Engineering Rice University Masters Master of Arts reformatted digital Thesis Math. 1973 Shapiro Shapiro, Michael Richard. "On the existence of kernel functions for the heat equation in n dimensions." (1973) Master’s Thesis, Rice University. https://hdl.handle.net/1911/104723.
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