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    Fast diffusion equations on riemannian manifolds
    (KHAYYAM PUBL CO INC, 2020) Bakim, Sumeyye; Goldstein, Gisele Ruiz; Goldstein, Jerome A.; Kombe, Ismail
    In the present paper, we first study the nonexistence of positive solutions of the following nonlinear parabolic problem {partial derivative u/partial derivative t = Delta g(u(m)) + V(x)u(m) + lambda u(q) in Omega x (0, T), u(x, 0) = u(0)(x) >= 0 in Omega, u(x, t) = 0 on partial derivative Omega x (0, T). Here, Omega is a bounded domain with smooth boundary in a complete non-compact Riemannian manifold M, 0 < m < 1, V is an element of L-loc(1)(Omega), q > 0 and A E R. Next, we prove some Hardy and Leray type inequalities with remainders on a Riemannian Manifold M. Furthermore, we obtain explicit (sometimes optimal) constants for these inequalities and present several nonexistence results with help of Hardy and Leray type inequalities on the hyperbolic space H-n.