Dear students/colleagues:
Click on the link of my web page for contact.
https://sites.google.com/view/ismailkombe/home
Education:
Ph.D. Mathematics, The University of Memphis, Memphis, TN, USA, 2003
M.A. Mathematics, The University of Pittsburgh, Pittsburgh, PA, USA, 1995
B.S. Mathematics, Ankara University, Ankara, TÜRKİYE, 1990
High School, Ankara Atatürk Lisesi, Ankara, TÜRKİYE, 1986
Biography:
Dr. Kömbe received his Ph.D. in 2003 from the University of Memphis under the direction of J. A. Goldstein. He spent one year as a post doctoral fellow at the University of Missouri. In 2004, he was appointed as an Assistant Professor at Oklahoma City University and then was promoted to Associate Professor in 2007, tenured in 2009 respectively at Oklahoma City University.
Dr. Kömbe’s research interests are in the Partial Differential Equations and Geometric Analysis. In April 2009, Dr. Kömbe received the Distinguished Achievement in the Scholarship of Discovery Award in recognition of excellence in disciplinary research at Oklahoma City University.
At the Oklahoma City University, Dr. Kömbe taught a wide range of mathematics courses, including College Algebra, Single Variable and Multivariable Calculus, Advanced Calculus, Differential Equations, Linear Algebra, Mathematical Statistics, Complex Variables, Discrete Mathematics, Real Variables, and Abstract Algebra.
Dr. Kömbe joined the faculty in the mathematics department at İstanbul Commerce University during the fall of 2011. He teaches a wide range of courses including Single Variable and Multivariable Calculus, Advanced Calculus, Differential Geometry, Real Analysis, Partial Differential Equations, Linear Algebra, Engineering Mathematics, Differential Equations. Besides undergraduate courses he also teaches graduate courses including Fourier Analysis and Boundary Value Problems, Measure Theory, Partial Differential Equations, Calculus on Manifolds, and Sobolev Spaces and Geometric Inequalities.
Dr. Kömbe’s current research interests include Hardy, Rellich and Heisenberg Uncertainty Principle type inequalities and their sharp versions on complete manifolds.
MathSciNet Links:
- authored by İsmail Kömbe
Publications:
→Years : 2011 — 2025:
43) Ismail Kombe, Sümeyye Bakım, Reyhan Tellioğlu, “Several Weighted Hardy, Hardy-Sobolev-Mazya and Related Inequalities” ,
https://arxiv.org/abs/2108.04522
42) Ismail Kombe “Some Nonlinear Parabolic Equations with Robin Boundary Conditions and Hardy-Leray type Inequalities on Riemannian Manifolds“, submitted for publication.
41) Ismail Kombe “The linear heat equation with Robin boundary condition and application of Hardy-Leray type inequalities on Riemannian Manifolds“, submitted for publication.
40) Ismail Kombe ” Nonlinear Parabolic Equations and Hardy-Leray type inequalities on Carnot groups“, submitted for publication.
39) Ismail Kombe ” Some Fast Diffusion Equations and Hardy-Leray type inequalities associated to Baouendi-Grushin operators “, submitted for publication.
38) Ismail Kombe ” Hardy-Leray type inequalities and p-Laplacian parabolic problems associated to Baouendi-Grushin operators “, submitted for publication.
37) Ismail Kombe and Sümeyye Bakım, “Doubly Nonlinear Parabolic Equations on Riemannian Manifolds“, submitted for publication.
36) Gisele Goldstein, Jerome Goldstein, Ismail Kombe, Abdel Aziz Randi ” Scaling and instantaneous blow up” Quaestiones Mathematicae vol.47, no.sup1, pp.169-177, 2024.
35) Gisele Goldstein, Jerome Goldstein, Ismail Kombe, “Non-existence results for p-Laplacian parabolic problems on the Heisenberg group ” Discrete and Continuous Dynamical Systems Ser. S 16(2023), no.9.2354-2363.
34) Gisele Goldstein, Jerome Goldstein, Ismail Kombe, “Non-existence results for nonlinear parabolic problems on the Heisenberg group ” To appear in Contemporary Mathematics, Amer. Math. Soc.
33) Ismail Kombe and Abdullah Yener, “Weighted Hardy Type inequalities with Robin Boundary Conditions“, Discrete and Continuous Dynamical Systems, 2023.
2022
32) Ismail Kombe, Reyhan Tellioğlu ” Doubly nonlinear parabolic equations with Robin boundary conditions” Mathematical Methods in Applied Sciences, 2022.
https://doi.org/10.1002/mma.8312
31) Gisele Goldstein, Jerome Goldstein, Ismail Kombe, Reyhan Tellioğlu “Nonexistence of positive solutions for nonlinear parabolic Robin problems and Hardy-Leray Inequalities” Annali di Matematica Pura ed Applicata, 2022.
https://doi.org/10.1007/s10231-022-01226-6
2021
30) Sümeyye Bakım, Gisele Goldstein, Jerome Goldstein, Ismail Kombe ” Nonexistence Results for Parabolic Equations
Involving the p-Laplacian and Hardy-Leray Type Inequalities on Riemannian Manifolds ” Journal of Evolution Equations, (21) 2, 2021.
29) Gisele Goldstein, Jerome Goldstein, Ismail Kombe, Reyhan Tellioğlu ” Nonlinear Parabolic Equations with Robin Boundary Conditions and Hardy-Leray Type Inequalities”, Stochastic Processes and Functional Analysis: New Perspectives, To appear in Contemporary Mathematics 774, Amer. Math. Soc., Providence, RI, 2021.
2020
28) Sümeyye Bakım, Gisele Goldstein, Jerome Goldstein, Ismail Kombe ” Fast Diffusion Equations on Riemannian Manifolds “, Differential and Integral Equations, 33(9-10), (2020), 507-526.
2018
27) Kombe, Ismail; Yener, Abdullah “A General Approach to weighted L^p-Rellich type inequalities related to Greiner operator”, Communications on Pure and Applied Analysis, 18(2), (2018), 869-886.
26) Kombe, Ismail; Yener, Abdullah “General weighted Hardy type inequalities related to Baouendi-Grushin operators”, Complex Variables and Elliptic Equations, 63(3), (2018), 420-436.
25) Goldstein, Jerome; Kombe, Ismail; Yener, Abdullah “A General Approach to Weighted Rellich Type inequalities on Carnot Groups”, Monatshefte für Mathematik, 186(1), (2018), 1-24.
24) Kombe, Ismail; Ahmetolan, Semra “Improved Hardy and Rellich type inequalities with two weight functions”, Mathematical Inequalities & Applications, Volume 21, Number 3 (2018), 885–896.
2017
23) Kombe, Ismail; Yener, Abdullah “Weighted Rellich type inequalities related to Baouendi-Grushin operators”, Proceedings of the American Mathematical Society, 145(11), 2017, 4845-4857.
22) Goldstein, Jerome; Kombe, Ismail; Yener, Abdullah ” A Unified Approach to Weighted Hardy Type inequalities on Carnot groups” Discrete and Continuous Dynamical Systems-Series A, 37(4), (2017), 2009-2021.
2016
21) Kombe, Ismail; Ahmetolan, Semra “Sharp Hardy and Rellich type inequalities with two weight”, Mathematical Inequalities & Applications, Volume 19, Number 3 (2016), 937–948.
20) Kombe, Ismail; Yener, Abdullah “Weighted Hardy and Rellich type inequalities on Riemannian manifolds”, Mathematische Nachrichten, 289 (2016), issue 8-9, 994-1004.
2015
19) Kombe, Ismail, “Hardy and Rellich-type inequalities with remainders for Baouendi-Grushin vector fields’’, Houston Journal of Mathematics, Volume 41, No.3 (2015), 849-873.
2013
18) Kombe, Ismail, “ On the nonexistence of positive solutions to Doubly Nonlinear equations for Baouendi-Grushin operators”, Discrete and Continuous Dynamical Systems-Series A (DCDS-A), Volume 33, Number 11&12, (2013), 5167-5176.
17) Kombe, Ismail; Özaydın, Murad, “Hardy-Poincare, Rellich and uncertainty principle inequalities on Riemannian manifolds”, Transactions of the American Mathematical Society, 365 (2013), 5035-5050.
2012
16) Kombe, Ismail; Ahmetolan, Semra, “Sharp uncertainty principle and Hardy-Poincaré inequalities on sub-Riemannian manifolds”, Mathematical Inequalities & Applications, Volume 15, Number 2 (2012), 457–467.
→Years: 2004 — 2011 (Oklahoma City University):
15) Kombe, Ismail, “Sharp weighted Rellich and uncertainty principle inequalities on Carnot groups”, Commun. Appl. Anal. 14 (2010), no. 2, 251–271.
14) Kombe, Ismail; Özaydin, Murad, “Improved Hardy and Rellich inequalities on Riemannian manifolds”, Trans. Amer. Math. Soc. 361 (2009), no. 12, 6191–6203.
13) Goldstein, Jerome A.; Kombe, Ismail, “The Hardy inequality and nonlinear parabolic equations on Carnot groups”, Nonlinear Anal. 69 (2008), no. 12, 4643–4653.
12) Goldstein, Jerome A.; Kombe, Ismail, “Gaussian estimates and instantaneous blowup”, Positivity 12 (2008), no. 1, 75–82.
11) Ruiz Goldstein, Gisèle; Goldstein, Jerome A.; Kombe, Ismail, “The power potential and nonexistence of positive solutions”, Differential equations: inverse and direct problems, 183–195, Lect. Notes Pure Appl. Math., 251, Chapman & Hall/CRC, Boca Raton, FL, 2006,
10) Kombe, Ismail, “Nonlinear degenerate parabolic equations for Baouendi-Grushin operators”, Math. Nachr. 279 (2006), no. 7, 756–773.
9) Kombe, Ismail, “On the nonexistence of positive solutions to nonlinear degenerate parabolic equations with singular coefficients”, Appl. Anal. 85 (2006), no. 5, 467–478.
8) Kombe, Ismail, “Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equations”, Abstr. Appl. Anal. 2005, no. 6, 607–617.
7) Goldstein, Gisele Ruiz; Goldstein, Jerome A.; Kombe, Ismail, “Nonlinear parabolic equations with singular coefficient and critical exponent”, Appl. Anal. 84 (2005), no. 6, 571–583.
6) Goldstein, Jerome A.; Kombe, Ismail, “Nonlinear degenerate parabolic equations on the Heisenberg group”, Int. J. Evol. Equ. 1 (2005), no. 1, 1–22.
→Years: 2004 — University of Missouri:
5) Kombe, Ismail, “The linear heat equation with highly oscillating potential”, Proc. Amer. Math. Soc. 132 (2004), no. 9, 2683–2691.
4) Kombe, Ismail “Doubly nonlinear parabolic equations with singular lower order term”, Nonlinear Anal. 56 (2004), no. 2, 185–199.
→Years: 1999 — 2003 (The University of Memphis):
3) Kombe, Ismail; “Linear and nonlinear parabolic partial differential equations with singular lower order term”, Thesis (Ph.D.)–The University of Memphis. 2003. 131 pp. ISBN: 978-0496-43293-6, ProQuest LLC, Thesis.
2) Goldstein, Jerome A.; Kombe, Ismail, “Nonlinear degenerate parabolic equations with the singular lower-order term”, Adv. Differential Equations 8 (2003), no. 10, 1153–1192.
1) Goldstein, Jerome A.; Kombe, Ismail, “Instantaneous blow up”, Advances in differential equations and mathematical physics (Birmingham, AL, 2002), 141–150, Contemp. Math., 327, Amer. Math. Soc., Providence, RI, 2003.