Publications

1.Duruk N, Erkip A, Erbay HA

“A higher-order Boussinesq equation in locally nonlinear theory of one-dimensional nonlocal elasticity”, IMA Journal of Applied Mathematics 74, 97-106 (2009).

2. Duruk N, Erkip A, Erbay HA

“Global existence and blow-up for the nonlocal nonlinear Cauchy problem arising in elasticity”, Nonlinearity 23, 107-118 (2010).

3. Duruk N, Erkip A, Erbay HA

“Blow-up and global existence for a general class of nonlocal nonlinear coupled wave  equations”, Journal of differential equations 250, 1448-1459 (2011).

4. Duruk Mutlubas N,

“On the Cauchy problem for a model equation for shallow water waves of moderate amplitude”, Nonlinear Analysis Real World Applications 14, 2022-2026 (2013).

5. Duruk Mutlubaş N, Geyer A, “Orbital stability of solitary waves of moderate amplitude in shallow water” , Journal of Differential Equations 255, 254-263 (2013).

6. Duruk Mutlubaş N, “Local well-posedness and wave breaking results for periodic solutions of a shallow water equation for waves of moderate amplitude”, Nonlinear Analysis: Theory Methods and Applications 97, 145-154 (2014).

7. Duruk Mutlubaş N, Geyer A, Matioc B-V, “Non-uniform continuity of the flow map for an evolution equation modeling shallow water waves of moderate amplitude”, Nonlinear Analysis Real World Applications 17, 322-331 (2014).

8. Duruk Mutlubaş N, “ On the Cauchy problem for the fractional Camassa-Holm equation”, Monatshefte für Mathematik, DOI: 1007/s00605-019-01278-6, 2019.

9. Duruk Mutlubaş N, Geyer A, Quirchmayr R, “Well posedness of a highly nonlinear shallow water equation on the circle”, Nonlinear Analysis, 2020, https://doi.org/10.1016/j.na.2020.111849.

10. Duruk Mutlubaş N, “Erratum to: On the Cauchy problem for a model equation for shallow water waves of moderate amplitude” [Nonlinear Anal. RWA 14 (5) (2013) 2022–2026], 10.1016/j.nonrwa.2019.103073.

11. Duruk Mutlubaş N, “Corrigendum to: Local well-posedness and wave breaking results for periodic solutions of a shallow water equation for waves of moderate amplitude”, 10.1016/j.na.2019.111712.

12. Duruk Mutlubaş N, Freire I, “The Cauchy problem and continuation of periodic solutions for a generalized Camassa-Holm equation”, 10.1080/00036811.2022.2057304, Applicable Analysis, 2022.

13. Duruk Mutlubas N, Freire I., “Existence and uniqueness of periodic pseudospherical surfaces emanating from Cauchy problems”, submitted.

14. Ayhan N, Duruk Mutlubas N, “On the Cauchy Problem for the Dispersion Generalized Camassa-Holm Equation”, submitted.

15. Duruk Mutlubaş N, İnci H, “Qualitative analysis of a new two-component system modeling shallow water waves”, in progress.

16. Duruk Mutlubaş N, Natali F, “Existence of periodic waves for the modified Degasperis-Procesi equation”, in progress.

17. Dhara R, Duruk Mutlubaş N, “Waves of maximal height for a class of negative-order dispersive equations”, in progress.

THESIS ADVISOR (Msc):

Nesibe Ayhan- Qualitative Analysis for the dispersion-generalized Camassa-Holm equation, 2022.

Burak Kardaş- Present.

ACADEMIC EVENTS

 

International Conference Publications

 

  1. Duruk Mutlubaş, “ The role of dispersive effect in qualitative analysis of nonlinear nonlocal equations”, Mathematics Days in Sofia, Bulgaria, 2023.

 

  1. Ayhan, N. Duruk Mutlubas, “Cauchy problem for the dispersion-generalized Camassa-Holm equation”, SIAM Conference on Nonlinear Waves and Coherent Structures, Bremen, Germany, 2022.

 

  1. Duruk Mutlubaş, I. Freire, “The Cauchy problem and continuation of periodic solutions for a generalized Camassa-Holm equation”, Conference on Mathematics of Wave Phenomena, Abstracts, Karlsruhe, Germany, 2022.

 

  1. Duruk Mutlubaş, “On the Periodic Solutions to a Highly Nonlinear Shallow Water Equation”, Equadiff 19, Abstracts, Leiden, Netherlands, 2019.

 

  1. Borluk, N. Duruk Mutlubaş, “On the stability of traveling wave solutions to the Fornberg-Whitham equation”, Conference on Mathematics of Wave Phenomena, Abstracts, Karlsruhe, Germany, 2018.

 

  1. Duruk Mutlubaş, “Cauchy problem for fractional-type Camassa-Holm equation”, Workshop on Nonlinear Pdes in Applied Mathematics, İzmir, Turkey, 2016.

 

  1. N. Duruk Mutlubaş, “ On the local well-posedness of fractional-type Camassa-Holm equation”, 7th European Congress of Mathematics, Berlin, Germany, 2016.

 

  1. Duruk Mutlubaş, H. A. Erbay, A. Erkip, “Some qualitative properties of a fractional-type Camassa-Holm equation”, Equadiff 15, Lyon, France, 2015.

 

  1. Duruk Mutlubaş, A. Geyer, “Orbital stability of solitary waves of moderate amplitude in shallow water”, SIAM Conference on Nonlinear Waves and Coherent Structures, Cambridge, UK, 2014 (Nonlinear Dispersive Wave Equations Minisymposium).

 

  1. Duruk Mutlubaş, “On periodic solutions of a model equation for surface waves of moderate amplitude in shallow water”, SIAM Conference on Nonlinear Waves and Coherent Structures, Cambridge, UK, 2014.

 

  1. Geyer, N. Duruk Mutlubaş, “Orbital stability of solitary waves of moderate amplitude in shallow water”, SIAM Conference on Analysis of Partial Differential Equations, Florida, ABD, 2013.

 

  1. Duruk Mutlubaş, “On periodic solutions of a model equation for surface waves of moderate amplitude in shallow water”, Equadiff 13, Prague, Czech Republic, 2013.

 

  1. Erkip, C. Babaoğlu, H. Borluk, N. Duruk, H. A. Erbay, S. Erbay, G. Muslu, “On some nonlocal nonlinear wave equations”, Workshop on Nonlocal Models and Peridynamics, Berlin, Germany, 2012.

 

  1. A. Erbay, N. Duruk and A. Erkip, “Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations”, SIAM Conference on Analysis of Partial Differential Equations, San Diego, USA, 2011.

 

  1. A. Erbay, N. Duruk, S. Erbay and A. Erkip, “Global existence and blow-up results for some problems in nonlinear nonlocal elasticity”, Mini-Workshop:Mathematical Analysis for Peridynamics, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany, 2011.

 

  1. Erkip, C. Babaoğlu, H. Borluk, N. Duruk, H. A. Erbay, S. Erbay and G. M. Muslu, “A review of some results on a class of nonlocal nonlinear wave-type Cauchy problems”, Nonlinear Dispersive Equations, Istanbul, Turkey, 2010.

 

  1. Duruk, H. A. Erbay and A. Erkip, “Blow-up and global existence for   a general class of nonlocal nonlinear coupled wave equations”, Nonlinear Dispersive Equations, Istanbul, Turkey, 2010.

 

  1. Duruk, H. A. Erbay and A. Erkip, “Global existence and blow-up for the nonlocal nonlinear Cauchy problem arising in elasticity”, ISAAC, Londra, UK, 2009.

 

  1. Duruk, A. Erkip and H. A. Erbay, “A higher-order Boussinesq equation in locally nonlinear theory of one-dimensional nonlocal elasticity, Nonlinear Dispersive Equations, Istanbul, Turkey, 2008.

 

  1. Erkip, N. Duruk and H. A. Erbay, “Cauchy problem for a higher-order Boussinesq equation”, Abstracts for ICIAM 07, page 366, 6th International Congress on Industrial and Applied Mathematics, Zurich, Switzlerland, 2007.

 

National Conference Publications

 

  1. Duruk Mutlubaş, “Yerel ve doğrusal olmayan dalga modellerinde dispersif etkinin matematiksel analizi”, 35. Ulusal Matematik Sempozyumu, Trakya University, Edirne, Turkey, 2023.

 

  1. Duruk Mutlubaş, “Kısmi türevli evolüsyon denklemleri için yarıgrup yaklaşımı”, XXVII. Ulusal Matematik Sempozyumu, Yeditepe University, İstanbul, Turkey, 2014 (Invited speaker for special session on Operator Theory).

 

  1. Duruk Mutlubaş, “Orta Dereceli Genlikte Yüzey Dalga Denklemlerinin Periyodik Çözümleri”, XXVI. National Mathematics Symposium, Diyarbakır, Turkey, 2013.

 

  1. Duruk, H. A. Erbay and A. Erkip, “Doğrusal olmayan kuple integro-diferansiyel dalga denklemleri için global varlık ve patlama”, XXIII. National Mathematics Symposium, Kayseri, Turkey, 2010.

 

  1. Duruk, H. A. Erbay and A. Erkip, “Yerel olmayan Cauchy problem ailesi için global varlık ve patlama”, XXII. National Mathematics Symposium, Selçuk, İzmir, Turkey, 2009.

 

  1. Duruk, H. A. Erbay and A. Erkip, “Yerel olmayan elastisite için bir Cauchy problemi”, XXI. National Mathematics Symposium, Istanbul, Turkey, 2008.

 

  1. Duruk, H. A. Erbay and A. Erkip, “Yüksek mertebe Boussinesq denklemi için Cauchy problemi”, XX. National Mathematics Symposium, Erzurum, Turkey, 2007.

 

 

 

 

 

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