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Study on zero sets of solutions of Heat Equations

Research Project

Project/Area Number 10640170
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionHyogo 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)
Keywordspartial 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. 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.

Report

(5 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (5 results)

All Other

All Publications (5 results)

  • [Publications] Kinji Watanabe: "Hermite Polynominals with two independent variables"Hyogo-Univ of Teacher Education Journal. 21-3. 1-9 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kinji Watanabe: "Hermite polynominals with two independent vfariables"Hyogo Univ. of Teacher Educations Journal. 21-3. 1-9 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kinji Watanabe: "Hermite Polynominals with Two independent variables"Hyogo Univ. of Teacher Education Journal. 21-3. 1-9 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kinji Watanabe: "Hermite polynominals with two independent variables"Hyogo University of Teacher Education Journal. 21巻(発表予定). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] 渡辺金治: "2階楕円型偏微分方程式の零解の零点の次数"数理解析研究所講究録. 1111. 97-101 (1999)

    • Related Report
      1999 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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