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

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  • Nakao Hayashi
    Research Alliance Center for Mathematical Sciences, Tohoku University, Sendai 980-8578, Japan. E-mail:
  • Elena I. Kaikina
    Centro de Ciencias Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán, Mexico. E-mails: ,
  • Pavel I. Naumkin
    Centro de Ciencias Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán, Mexico. E-mails: ,
  • Takayoshi Ogawa
    Mathematical Institute, Tohoku University, Sendai 980-8578, Japan. E-mail:

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<jats:p> We study the nonlinear Neumann boundary value problem for semilinear heat equation [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] is small enough. We investigate the life span of solutions for [Formula: see text]. Also we study the global in time existence and large time asymptotic behavior of solutions in the case of [Formula: see text] and [Formula: see text]. </jats:p>

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