I am a Professor of Mathematics in the Department of Mechatronics Engineering at Istanbul Commerce University.

**This semester, Fall 2021, I am teaching:**

Although all classes are remote, I continue to teach my classes in my own classroom to make learning easier and to be closer to my students. Here are some recent pictures from my class:

Mathematical Analysis-2 and Matematik Analiz 4

The homework component of your grade in courses MAT 121and ENG 126 are determined by online **WeBWorK assignments. Enter the url http://webwork.ticaret.edu.tr/webwork2/ in your web browser. You should see a list of available courses. To find your course, you will need to know your course code (i.e , MAT 122, ENG126, ENG227,..) , year and semester.**

My office is B205 (Küçükyalı), and my office hours are

- Monday &Thursday: 1 pm-3 pm.
- also by appointment.

Please stop by to say hi!

## Message to Students

Dear students:

As the rest of humanity, we are going through difficult times that require proactive measures from every individual. Please understand the importance of social distancing and hygiene to fight this virus. This is no joke, please do not get out of your houses unless necessary. Wear a mask and gloves when you have to go outside. Remember to wash your hands often for 20 seconds and try to keep your houses clean. Make sure to clean whatever you buy from outside.

Prof. Dr. İsmail Kömbe

Küçükyalı E5 Kavşağı İnönü Cad. No: 4,

Küçükyalı 34840 / İstanbul

Phone: TBA

Office: B205

E-mail:**ikombe**[at]

**ticaret**(dot)

**edu**(dot)

**tr,**

**ikombe40**[at]

**gmail**(dot)

**com**

**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 — İstanbul Commerce Univesity:

32) Kombe, Ismail ” Fourth Order Partial Differential Equations with Singular Lower Order Term on Riemannian Manifolds ” (submitted)

31) Gisele Goldstein, Jerome Goldstein, Ismail Kombe, Reyhan Tellioğlu ” Nonexistence of positive solutions for nonlinear

parabolic Robin problems and Hardy-Leray Inequalities” To appear in **Annali di Matematica Pura ed Applicata, 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.*

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.**

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.**

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.**

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.**

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.**

** **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.**

*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.

**Ph. D Students: **

- Abdullah Yener graduated in July 2017. He is currently an Assistant Professor at Istanbul Commerce University, Istanbul, Turkey.
- Sümeyye Bakım graduated in July 2021. She is currently an Assistant Professor at KTO Karatay University, Konya, Turkey.
- Reyhan Tellioğlu is a graduate student at Istanbul Commerce University.

**Master of Science Students: **

- Abdullah Yener graduated in July 2013.
- Erkan Gürsu graduated in July 2017.

**Teaching: **

I love teaching and that is one of the main reasons I am at Istanbul Commerce University. You can reach my course web pages via the above links. The following is a list of classes that I have taught at Oklahoma City University (OCU) and İstanbul Commerce University.

2004-2005 (Oklahoma City University) | Fall |
College Algebra |

College Algebra | ||

Calculus and Analytic Geometry I | ||

Calculus III | ||

Spring |
College Algebra | |

College Algebra | ||

Calculus and Analytic Geometry II | ||

Real Variables | ||

2005-2006 (OCU) | Fall |
College Algebra |

Abstract Algebra | ||

Calculus and Analytic Geometry I | ||

Calculus III | ||

Spring |
College Algebra | |

College Algebra | ||

Calculus and Analytic Geometry II | ||

Differential Equations | ||

2006-2007 (OCU) | Fall |
College Algebra |

Advanced Calculus | ||

Calculus and Analytic Geometry I | ||

Calculus III | ||

Spring |
College Algebra | |

College Algebra | ||

Calculus and Analytic Geometry II | ||

Differential Equations | ||

2006-2007 (OCU) | Fall |
College Algebra |

Abstract Algebra | ||

Calculus and Analytic Geometry I | ||

Calculus III | ||

Spring |
Complex Variables | |

College Algebra | ||

Calculus and Analytic Geometry II | ||

Differential Equations | ||

2007-2008 (OCU) | Fall |
College Algebra |

Abstract Algebra | ||

Calculus and Analytic Geometry I | ||

Calculus III | ||

Spring |
College Algebra | |

Discrete Mathematics | ||

Calculus and Analytic Geometry II | ||

Differential Equations | ||

2008-2009 (OCU) | Fall |
College Algebra |

Linear Algebra | ||

Calculus and Analytic Geometry I | ||

Calculus III | ||

Spring |
College Algebra | |

College Algebra | ||

Calculus and Analytic Geometry II | ||

Differential Equations | ||

2009-2010 (OCU) | Fall |
College Algebra |

Abstract Algebra | ||

Calculus and Analytic Geometry I | ||

Probability and Statistics I | ||

Spring |
College Algebra | |

College Algebra | ||

Calculus and Analytic Geometry I | ||

Differential Equations | ||

2010-2011 (Oklahoma City University) | Fall |
College Algebra |

College Algebra | ||

Calculus and Analytic Geometry II | ||

Calculus III | ||

Introduction to Differential Geometry (Independent study) | ||

Spring |
College Algebra | |

Complex Variables | ||

Calculus and Analytic Geometry I | ||

Linear Algebra | ||

Introduction to Measure and Integral (Capstone course) |

**Istanbul Commerce University**

*Spring*

2011-2012 (Istanbul Commerce University) |
Fall |
Kısmi Türevli Denklemler |

Diferansiyel Geometri | ||

Matematiksel İstatistik | ||

Ayrık Matematik | ||

Business Statistics( 2 section) | ||

Mesleki İngilizce I | ||

Uygulamalı Matematik I(Graduate) | ||

Spring |
Reel Analiz | |

Mesleki İngilizce II | ||

Mühendislik Matematiği ( 2 section) | ||

Uygulamalı Matematik II(Graduate) | ||

2012-2013 (Istanbul Commerce University) | Fall |
Kısmi Türevli Denklemler |

Mesleki İngilizce I | ||

Business Statistics | ||

Matematik Analiz III | ||

Ölçüm Teorisi (Graduate) | ||

Spring |
Matematik Analiz IV | |

Reel Analiz I | ||

Diferansiyel Geometri | ||

Linear Algebra | ||

İleri Kısmi Diferansiyel Denklemler(Graduate) | ||

2013-2014 (Istanbul Commerce University) | Fall |
Kısmi Türevli Denklemler I |

Mathematical Analysis I | ||

Matematik I | ||

Matematik Analiz III | ||

2013-2014 (Istanbul Commerce University) | Spring |
Diferansiyel Geometri |

Mathematical Analysis II | ||

Mesleki İngilizce | ||

Matematik Analiz IV | ||

Sobolev uzayları ve Geometrik Eşitsizlikler(Graduate) | ||

2014-2015 (Istanbul Commerce University) | Fall |
Kısmi Türevli Denklemler I |

Mathematical Analysis I | ||

Mathematics I | ||

Mesleki İngilizce I | ||

Ölçüm Teorisi (Graduate) | ||

Spring |
Diferansiyel Geometri | |

Mathematical Analysis II | ||

Mathematics II | ||

Mesleki İngilizce II | ||

Matematik Analiz IV | ||

2015-2016 (Istanbul Commerce University) | Fall |
Kısmi Türevli Denklemler I |

Mathematical Analysis I | ||

Mathematics I | ||

Mesleki İngilizce I | ||

Ölçüm Teorisi (Graduate) | ||

Spring |
Diferansiyel Geometri | |

Mathematical Analysis II | ||

Mathematics II | ||

Advanced Engineering Mathematics(Graduate) | ||

Matematik Analiz IV | ||

2016-2017 (Istanbul Commerce University) | Fall |
Kısmi Türevli Denklemler I |

Mathematical Analysis I | ||

Mathematics I | ||

Mesleki İngilizce I | ||

Ölçüm Teorisi (Graduate) | ||

Spring |
Engineering Mathematics II | |

Mathematical Analysis II | ||

Engineering Mathematics I | ||

2017-2018 (Istanbul Commerce University) | Fall |
Engineering Mathematics I |

Mathematical Analysis I | ||

Engineering Mathematics II | ||

Geometrik Analiz(Graduate) | ||

Spring |
Engineering Mathematics I | |

Mathematical Analysis II | ||

Engineering Mathematics II | ||

2019-2020 (Istanbul Commerce University) | Fall |
Engineering Mathematics I |

Mathematical Analysis I (2 section) | ||

Matematik Analiz IV | ||

Spring |
||