Nonlinear Neumann boundary value problem for semilinear heat equations with critical power nonlinearities

DOI Web Site 参考文献12件
  • Nakao Hayashi
    Research Alliance Center for Mathematical Sciences, Tohoku University, Sendai 980-8578, Japan. E-mail: nakao.hayashi.e6@tohoku.ac.jp
  • Elena I. Kaikina
    Centro de Ciencias Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán, Mexico. E-mails: ekaikina@matmor.unam.mx, pavelni@matmor.unam.mx
  • Pavel I. Naumkin
    Centro de Ciencias Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán, Mexico. E-mails: ekaikina@matmor.unam.mx, pavelni@matmor.unam.mx
  • Takayoshi Ogawa
    Mathematical Institute, Tohoku University, Sendai 980-8578, Japan. E-mail: ogawa@math.tohoku.ac.jp

説明

<jats:p>We study the nonlinear Neumann boundary value problem for semilinear heat equation ∂ t u − Δ u = λ | u | p , t > 0 , x ∈ R + n , u ( 0 , x ) = ε u 0 ( x ) , x ∈ R + n , − ∂ x u ( t , x ′ , 0 ) = γ | u | q ( t , x ′ , 0 ) , t > 0 , x ′ ∈ R n − 1 where p = 1 + 2 n , q = 1 + 1 n and ε > 0 is small enough. We investigate the life span of solutions for λ , γ > 0. Also we study the global in time existence and large time asymptotic behavior of solutions in the case of λ , γ < 0 and ∫ R + n u 0 ( x ) d x > 0.</jats:p>

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