Full entry |
PDF
(0.4 MB)
Feedback

optimal control; Pennes' bioheat equation; semigroup theory; thermal therapy; hyperthermia

References:

[1] Aghayan, S. A., Sardari, D., Mahdavi, S. R. M., Zahmatkesh, M. H.: **An inverse problem of temperature optimization in hyperthermia by controlling the overall heat transfer coefficient**. Hindawi Publishing Corporation J. Appl. Math. 2013 (2013), 1-9. MR 3090615

[2] Curtain, R. F., Zwart, H.: **An Introduction to Infinite-Dimensional Linear Systems Theory**. Springer-Verlag 21 of Text in Applied Mathematics, 1995. MR 1351248 | Zbl 0839.93001

[3] Cheng, K. S., Stakhursky, V., Craciunescu, O. I., Stauffer, P., Dewhirst, M., Das, S. K.: **Fast temperature optimization of multi-source hyperthermia applicators with reduced-order modelling of 'virtual sources'**. Physics in Medicine and Biology 53 (2008), 6, 1619-1635. DOI 10.1088/0031-9155/53/6/008

[4] Deng, Z. S., Liu, J.: **Analytical Solutions to 3D Bioheat Transfer Problems with or without Phase Change**. In: Heat Transfer Phenomena and Applications (S. N. Kazi, ed.), Chapter 8, InTech, 2012.

[5] Deng, Z. S., Liu, J.: **Analytical study on bioheat transfer problems with spatial or transient heating on skin surface or inside biological bodies**. J. Biomech. Eng. 124 (2002), 638-649. DOI 10.1115/1.1516810

[6] Dhar, R., Dhar, P., Dhar, R.: **Problem on optimal distribution of induced microwave by heating probe at tumour site in hyperthermia**. Adv. Model. Optim. 13 (2011), 1, 39-48. MR 2889921

[7] Dhar, P., Dhar, R., Dhar, R.: **An optimal control problem on temperature distribution in tissue by induced microwave**. Adv. Appl. Math. Biosciences 2 (2011), 1, 27-38.

[8] Dhar, P., Dhar, R.: **Optimal control for bio-heat equation due to induced microwave**. Springer J. Appl. Math. Mech. 31 (2010), 4, 529-534. DOI 10.1007/s10483-010-0413-x | MR 2647997 | Zbl 1205.49004

[9] Gomberoff, A., Hojman, S. A.: **Non-standard construction of Hamiltonian structures**. J. Phys. A: Math. Gen. 30 (1997), 14, 5077-5084. DOI 10.1088/0305-4470/30/14/018 | MR 1478610 | Zbl 0939.70020

[10] Heidari, H., Malek, A.: **Optimal boundary control for hyperdiffusion equation**. Kybernetika 46 (2010), 5, 907-925. MR 2778921 | Zbl 1206.35138

[11] Heidari, H., Zwart, H., Malek, A.: **Controllability and Stability of 3D Heat Conduction Equation in a Submicroscale Thin Film**. Department of Applied Mathematics, University of Twente, Enschede 2010, pp. 1-21.

[12] Karaa, S., Zhang, J., Yang, F.: **A numerical study of a 3D bioheat transfer problem with different spatial heating**. Math. Comput. Simul. 68 (2005), 4, 375-388. DOI 10.1016/j.matcom.2005.02.032 | MR 2141455 | Zbl 1062.92018

[13] Loulou, T., Scott, E. P.: **Thermal dose optimization in hyperthermia treatments by using the conjugate gradient method**. Numer. Heat Transfer, Part A 42 (2002), 7, 661-683. DOI 10.1080/10407780290059756

[14] Malek, A., Bojdi, Z., Golbarg, P.: **Solving fully 3D microscale dual phase lag problem using mixed-collocation, finite difference discretization**. J. Heat Transfer 134 (2012), 9, 094501-094506. DOI 10.1115/1.4006271

[15] Malek, A., Nataj, R. Ebrahim, Yazdanpanah, M. J.: **Efficient algorithm to solve optimal boundary control problem for Burgers' equation**. Kybernetika 48 (2012), 6, 1250-1265. MR 3052884

[16] Malek, A., Momeni-Masuleh, S. H.: **A mixed collocation-finite difference method for 3D microscopic heat transport problems**. J. Comput. Appl. Math. 217 (2008), 1, 137-147. DOI 10.1016/j.cam.2007.06.023 | MR 2427436 | Zbl 1148.65082

[17] Momeni-Masuleh, S. H., Malek, A.: **Hybrid pseudo spectral-finite difference method for solving a 3D heat conduction equation in a submicroscale thin film**. Numer. Methods Partial Differential Equations 23 (2007), 5, 1139-1148. DOI 10.1002/num.20214 | MR 2340665