Publications

Doctoral Thesis

1. Tzanetis D. E., “Global existence and asymptotic behaviour of unbounded solutions for the semilinear heat equation”, Ph. D. Thesis, Heriot-Watt University, Edinburgh, May 1986.

Publications in Refereed Journal

2. Lacey A. A. and Tzanetis D. E., “Global existence and convergence to a singular steady state for a semilinear heat equation”, Proceedings of the Royal Society of Edinburgh, 105A, 289-305, (1987).

3. Lacey A. A., Tzanetis D. E., “Complete Blow-Up for a semilinear diffusion equation with a sufficiently large initial condition”, IMA Journal of Applied Mathematics, 41, 207-215, (1988).

4. Lacey A. A., Tzanetis D. E., “Global, Unbounded Solutions to a Parabolic Equation”, Journal of Differential Equations, 101, 80-102, (1993).

5. Tzanetis D. E., “Asymptotic behaviour and blow-up of some unbounded solutions for a semilinear heat equation”, Proceedings of the Edinburgh Mathematical Society, 39, 81-96, (1996).

6. Lacey A. A., Tzanetis D. E. and Vlamos P. M., “Behaviour of a non-local reactive convective problem modelling Ohmic heating of foods”, Quarterly Journal of Mechanics and Applied Mathematics, 52, (4), (1999), 623-644.

7. Tzanetis D. E., Vlamos P. M., “A non-local problem modelling Ohmic heating with variable thermal conductivity”, Nonlinear Analysis: Real World Applications, (2001), 2, 443-454.

8. Tzanetis D. E. and Vlamos P. M., “Some interesting special cases of a non-local problem modelling Ohmic heating with variable thermal conductivity”, Proceedings of the Edinburgh Mathematical Society, 44, (2001), 585-595. 

9. Kavallaris N. I., Tzanetis D. E., “Blow-up and stability of a non-local diffusion-convection problem arising in Ohmic heating of foods”, Differential and Integral Equations, Vol. 15, N. 3, (2002), 271-288.

10. Kavallaris N. I., Nikolopoulos C.V. and Tzanetis D. E., “Estimates of blow-up time for a non-local problem modelling an Ohmic heating process”, European Journal of Applied Mathematics, (2002) , Vol. 13 pp. 337-351.

11. Tzanetis D. E., “Blow-up of radially symmetric solutions of a non-local problem modelling Ohmic heating”, Electronic Journal of Differential Equations, Vol. 2002(2002), No. 11, pp. 1-26.

12. Kavallaris N. I. and Tzanetis D. E., “An Ohmic heating nonlocal diffusion-convection problem for the Heaviside function”, Australian and New Zealand Industrial and Applied Mathematics Journal (Electronic Version), (2002), pp. E114-E142.

13. Kavallaris, N. I. and Tzanetis D. E., “Behaviour of critical solutions of a non-local hyperbolic problem in Ohmic heating of foods.” Appl. Math. E-Notes 2 (2002), 59-65 (electronic).

14. Nikolopoulos C. V., Tzanetis D. E., “A model for housing allocation of homeless population due to a natural disaster”, Nonlinear Analysis: Real World Applications (2003), no. 4, 561-579.

15. Kavallaris N. I., Lacey A. A. and Tzanetis D. E., “Global existence and divergence of critical solutions of a non-local parabolic problem in Ohmic heating process”. Nonlinear Anal. Theory Methods and Applications, 58 (2004), no. 7-8, 787-812.

16. Kavallaris N. I. and Tzanetis D. E., “Behaviour of a non-local reactive-convective problem with variable velocity in ohmic heating of food. Nonlocal elliptic and parabolic problems”, 189-198, Banach Center Publ., 66, Polish Acad. Sci., Warsaw, (2004).

17. Nikolopoulos C. V. and Tzanetis D. E., “Blow-up time estimates for a non-local reactive-convective problem modelling sterilization of food. Nonlocal elliptic and parabolic problems”, 237-250, Banach Center Publ., 66, Polish Acad. Sci., Warsaw, (2004).

18. Nikolopoulos C. V., Tzanetis D. E., “Estimates of blow-up time for a non-local reactive-convective problem modelling ohmic heating of foods.” Proc. Edinb. Math. Soc. (2) 49 (2006), no. 1, 215-239.

19. Kavallaris N. I., Tzanetis D. E., “On the blow-up of a non-local parabolic problem”.  Appl. Math. Lett.  19 (2006), 921-925.

20. Kavallaris N. I., Lacey A. A., Nikolopoulos C. V. and Tzanetis D. E., “Asymptotic analysis and estimates of blow-up time for the radial symmetric semilinear heat equation in the open-spectrum case,” Mathematical Methods in Applied Sciences, Vol 30, No 13, (2007), 1507 – 1526.

21. Politikos D.B., Tzanetis D. E. “Population Dynamics of the Mediterranean Monk Seal in the National Marine Park of Alonissos, Greece.” Mathematical and Computing Modelling, (2009), 505-515.

22. Latos E. A., Tzanetis D. E., “Existence and Blow-up of solutions for a            nonlocal Filtration and Porous Medium problem.” Proceedings of Edinburgh   Mathematical Society, (2) 53 (2010), no.1, 195-209.

23. Latos E. A., Tzanetis D. E., “Grow-up of critical solutions for a non-local porous medium problem with Ohmic heating source,” Nonlinear Differential Equations and Applications, 17, (2010), no. 2, 137-151.

24. Politikos D.B., Tzanetis D. E., Nikolopoulos C. V , Maravelias. “The     application of an age-structured model to the north Aegean anchovy fishery: an evaluation of different management measures”, Mathematical Biosciences, 237 (1-2), 17-27, (2012).

25. Latos E. A., Tzanetis D. E., Existence and blow-up of solutions for a semilinear filtration problem. Elec.  J. Diff. Eqs 2013, No. 178, 20 pp.

26. Kavallaris N. I., Lacey A. A., Nikolopoulos C. V. and Tzanetis D. E.,  A hyperbolic non-local problem modelling MEMS technology.  Rocky   Mountain J. Math. 41 (2011), no. 2, 505–534.

27. Kavallaris N. I., Lacey A. A., Nikolopoulos C. V. and Tzanetis D. E.,  “On the Quenching Behaviour of a Semilinear Wave Equation Modelling  MEMS Technology”, Discrete and Continuous Dynamical Systems-Series A, Vol. 35, No. 3, 13, 2015, p. 1009-1037.

28. D.V. Politikos,a, C.D. Maravelias and D.E. Tzanetis, Assessing the risk of alternative management strategies in a Mediterranean fishery: protecting the younger vs reducing fishing effort. J Biological Dynamics. 2013 Dec; 7(1): 183–198.

 

Some Publications in Conferences Proceedings

1. Lacey A. A., Tzanetis D. E. and Vlamos P. M., “Global existence and finite-time blow-up of a non-local hyperbolic problem modelling Ohmic heating of foods”, Proceedings of the 3rd International Workshop on Applied Mathematics in Science and Modern Technology, Metsovo, Greece, 30/6– 1/7, 1997, Pitman Research Notes in Mathematics Series, (1998), 390, p. 20-32.

2. Kavallaris N. I., Tzanetis D. E., “Behaviour of solutions of a non-local diffusion-convection problem of the Ohmic heating process, Proceedings of the 4th International Workshop on Mathematical Methods in Scattering  Theory and Biomedical Technology, October 8-10, 1999, Perdika, Thesprotia, Greece, World Scientific Publishing Co., Inc., (2000), p. 144-150.

3. Kavallaris N. I., Nikolopoulos C. V. and Tzanetis D. E., “An estimate of blow-up time for the solution of a non-local Ohmic heating problem”, International Conference on Mathematical Analysis and its Applications, August 24-27, 2000, In memoriam Christos Papakyriakopoulos,  Athens, Greece.

4. Kavallaris N. I., Nikolopoulos C. V. and Tzanetis D. E., “Upper and lower bounds of blow-up time in a non-local thermistor problem”, Proceedings of the 5th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Technology, October 18-19, 2001, Corfu, Greece, World Scientific Publishing Co., Inc.

5. Kavallaris N. I., Tzanetis D. E., “Global in time  unbounded solutions for a nonlocal thermistor problem”, Proceedings of the 5th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Technology, October 18-19, 2001, Corfu, Greece, World Scientific Publishing Co. Inc.

6. Kavallaris N. I., Tzanetis D. E., “Global existence and blow-up of solutions for a class of nonlocal problems with nonlinear diffusion”, Proceedings of the 6th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Technology, September 18 –21, 2003, Tsepelovo, Epirus, Greece, World Scientific Publishing Co. Inc.

7. Kavallaris N. I., Nikolopoulos C. V. and Tzanetis D. E., “Estimates of blow-up time for the “open-spectrum” case for the radial symmetric semilinear heat equation”, Proceedings of The International Conference on Numerical Analysis and Applied Mathematics (ICNAAM p.201-203, 2004), Chalkis, 10-14 September 2004, Greece, WILEY-VCH  Publications.

8. Nikolopoulos C. V., Tzanetis D. E., “A Mathematical Model for Housing Allocation of the Homeless Population due to the Earthquake of September 1999 in Athens”, “Proceedings of the “Influence of Traditional Mathematics and Mechanics on Modern Science and Technology”, p.433-438, May 24-28, 2004, Messini, Greece.

9. Kavallaris N. I., Nikolopoulos C. V. and Tzanetis D. E., “Estimates of blow-up time for the radial symmetric semilinear heat equation in the ‘open-spectrum’ case”. Finite volumes for complex applications IV, 237--246, ISTE, London, 2005.

 

School of Mathematical and Physical Sciences, Department of Mathematics Dimitrios E. Tzanetis

National Technical University of Athens