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  • Küçük Resim
    Öğe
    Nonexistence of positive solutions for nonlinear parabolic Robin problems and Hardy–Leray inequalities
    (Institute for Ionics, 2022) Goldstein, Gisèle Ruiz; Goldstein, Jerome A.; Kömbe, Ismail; Tellioğlu, Reyhan
    The purpose of this paper is twofold. First is the study of the nonexistence of positive solutions of the parabolic problem {?u?t=?pu+V(x)up-1+?uqin?×(0,T),u(x,0)=u0(x)?0in?,|?u|p-2?u??=?|u|p-2uon??×(0,T),where ? is a bounded domain in RN with smooth boundary ??, ?pu= div (| ? u| p-2? u) is the p-Laplacian of u, V?Lloc1(?), ??Lloc1(??), ?? R, the exponents p and q satisfy 1 < p< 2 , and q> 0. Then, we present some sharp Hardy and Leray type inequalities with remainder terms that provide us concrete potentials to use in the partial differential equation we are interested in.
  • Küçük Resim
    Öğe
    Scaling and instantaneous blow up
    (Taylor and Francis Ltd., 2024) Goldstein, Gisèle Ruiz; Goldstein, Jerome A.; Kömbe, İsmail; Rhandi, Abdelaziz
    The main result is a simple proof of the Baras-Goldstein (1984) instantaneous blow up result for the heat equation with the inverse square potential. The proof relies heavily, indeed mainly, on scaling. Remarks are also given concerning the case when the underlying space ?N is replaced by the Heisenberg group ?N.