Yazar "Kombe, Ismail" seçeneğine göre listele

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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.
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    Non-existence results for p-laplacian parabolic problems on the heisenberg group Hn
    (American Institute of Mathematical Sciences, 2023) Goldstein, Gisele Ruiz; Goldstein, Jerome A.; Kombe, Ismail
    Let Hn = Cn R be the 2n+1-dimensional Heisenberg group and be a bounded domain with smooth boundary @ in Hn. This paper deals with the nonexistence of positive solutions to the problem(Formula Presented) where Lu is the subelliptic p-Laplacian operator on the Heisenberg group Hn, p > 1, 2 R, s > 0, V 2 L1 loc(), 2 R and q > 0. We also demonstrate several applications of our main result using concrete potentials with sharp constants derived from Hardy and Leray type inequalities.
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    Nonlinear parabolic equations with Robin boundary conditions and Hardy-Leray type inequalities
    (Amer Mathematical Soc, 2021) Goldstein, Gisele; Goldstein, Jerome; Kombe, Ismail; Balekoglu, Reyhan Tellioglu
    We are primarily concerned with the absence of positive solutions of the following problem, {partial derivative u/partial derivative t = Delta (u(m)) + V (x) u(m) + lambda u(q) in Omega x (0, T), u(x, 0) = u(0)(x) >= 0 in Omega, {partial derivative u/partial derivative v = beta(x)u on partial derivative Omega x (0, T), where 0 < m < 1, V is an element of L-loc(1) (Omega), beta is an element of L-loc(1)(partial derivative Omega), lambda is an element of R, q > 0, Omega subset of R-N is a bounded open subset of R-N with smooth boundary partial derivative Omega, and partial derivative u/partial derivative v is the outer normal derivative of u on partial derivative Omega. Moreover, we also present some new sharp Hardy and Leray type inequalities with remainder terms that provide us concrete potentials to use in the partial differential equation of our interest.