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Nonlinear partial differential equation, parabolic type equation, delayed equation, system of partial differential equation, initial problem

References:

[1] Benhammouda, B., Vazquez-Leal, H.: **A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations**. SpringerPlus, (2016), 5, 1723. DOI 10.1186/s40064-016-3386-8. DOI 10.1186/s40064-016-3386-8

[2] Khan, Y., Svoboda, Z., Šmarda, Z.: **Solving certain classes of Lane-Emden type equations using the differential transformation method**. Advances in Difference Equations, 174, (2012). MR 3016691

[3] Odibat, Z. M., Bertelle, C., Aziz-Alaouic, M. A., Duchampd, H. E. G.: **A multi-step differential transform method and application to non-chaotic or chaotic systems**. Computers and Mathematics with Applications, 59, (2010), pp. 1462-1472. DOI 10.1016/j.camwa.2009.11.005 | MR 2591936

[4] Odibat, Z. M., Kumar, S., Shawagfeh, N., Alsaedi, A., Hayat, T.: **A study on the convergence conditions of generalized differential transform method**. Mathematical Methods in the Applied Sciences, 40, (2017), pp 40-48. DOI 10.1002/mma.3961 | MR 3583033

[5] Polyanin, A. D., Zhurov, A. I.: **Functional constraints method for constructing exact solutions to delay reactiondiffusion equations and more complex nonlinear equations**. Commun. Nonlinear Sci. Numer. Simulat., 19, (2014), pp 417-430. DOI 10.1016/j.cnsns.2013.07.017 | MR 3111621

[6] Rebenda, J., Šmarda, Z.: **A differential transformation approach for solving functional differential equations with multiple delays**. Commun. Nonlinear Sci. Numer. Simulat., 48, (2017), pp. 246-257. DOI 10.1016/j.cnsns.2016.12.027 | MR 3607372

[7] Rebenda, J., Šmarda, Z., Khan, Y.: **A New Semi-analytical Approach for Numerical Solving of Cauchy Problem for Differential Equations with Delay**. FILOMAT, 31, (2017), pp. 4725-4733. DOI 10.2298/FIL1715725R | MR 3725533