Study on zero sets of solutions of Heat Equations
Project/Area Number  10640170 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Basic analysis

Research Institution  Hyogo University of Teacher Education 
Principal Investigator 
WATANABE Kinji Hyogo Univ. of Teacher Education, Professor, 学校教育学部, 教授 (20004468)

Project Period (FY) 
1998 – 2001

Project Status 
Completed(Fiscal Year 2001)

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)

Keywords  partial differential equations / Heat equations / zero sets / Heat equation / partial differential aquation / Partial differential equations / strong uniqueness 
Research Abstract 
The following results are obtained and partially published in Hyogo University of Teacher Education Journal, vol. 21, No 3, (2001), pp. 19. 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.

Report
(5results)
Research Output
(5results)