Decay rates of the derivatives of the solutions of the heat equations in the exterior domain of a ball

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Abstract

We consider the initial-boundary value problem <br>(<i>P</i>) {$¥frac{∂}{∂<i>t</i>}$<i>u</i> = Δ<i>u</i>-<i>V</i>(|<i>x</i>|)<i>u</i>   in Ω<sub><i>L</i></sub>×(0,∞), <br>μ<i>u</i>+(1-μ)$¥frac{∂}{∂ν}$<i>u</i> = 0   on ∂Ω<sub><i>L</i></sub>×(0,∞), <br><i>u</i>(·,0) = φ(·)∈<i>L</i><sup><i>p</i></sup>(Ω<sub><i>L</i></sub>),   <i>p</i>≥1,<br>where Ω<sub><i>L</i></sub>={<i>x</i>∈<b><i>R</i></b><sup><i>N</i></sup>:|<i>x</i>|>L}, <i>N</i>≥2, <i>L</i>>0, 0≤μ≤1, &\u; is the outer unit normal vector to ∂Ω<sub><i>L</i></sub>, and <i>V</i> is a nonnegative smooth function such that <i>V</i>(<i>r</i>)=<i>O</i>(<i>r</i><sup>-2</sup>) as <i>r</i>→∞. In this paper, we study the decay rates of the derivatives ∇<sub><i>x</i></sub><sup><i>j</i></sup><i>u</i> of the solution <i>u</i> to (<i>P</i>) as <i>t</i>→∞.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 59(3), 861-898, 2007-07-01

    The Mathematical Society of Japan

References:  11

Cited by:  1

Codes

  • NII Article ID (NAID)
    10019540137
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    Journal Article
  • ISSN
    00255645
  • NDL Article ID
    8823404
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  CJPref  NDL  J-STAGE 
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