| Budget Amount *help |
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2001: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2000: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1999: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1998: ¥400,000 (Direct Cost: ¥400,000)
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| Research Abstract |
The following results are obtained and partially published in Hyogo University of Teacher Education Journal, vol. 21, No 3, (2001), pp. 1-9.
Let u(t, x, y) be an analytic solution of second order parabolic equations defined in neigbourhood of the origin (0, 0, 0) with two spatial dimension and let Z(t) be its zero sets, dependent on time varialble t, in some neighborhood of the origin (0, 0). Then one of the main results is the following. (1). When Z(t) is topologically homeomorphic to Z(0) for sufficiently small -t > 0 , then Z(t) is topologically homeomorphic to Z(Q) for sufficiently small t > 0. (2). Converse statement is holds under some assumptions.
To prove these, it is useful to study on zero sets of Hermite polynomials with two independent variables and their conjugate Hermite polynomials, which determine the initial form of u(t, x, y) in some sense.
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