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Exact Solutions > Nonlinear Delay Partial Differential Equations

Nonlinear Delay Partial Differential Equations

Some papers:

• J. Wu, X. Zou. Traveling wave fronts of reaction-diffusion systems with delay. J. Dynamics and Differential Equations, Vol. 13, pp. 651-687, 2001. (File of the article is taken from the Internet, see http://www.apmaths.uwo.ca/~xzou/Repr/jdde01.pdf)
• J. Huang, X. Zou. Traveling wavefronts in diffusive and cooperative Lotka-Volterra system with delays. J. Math. Anal. Appl., Vol. 271, pp. 455-466, 2002. (File of the article is taken from the Internet, see http://www.apmaths.uwo.ca/~xzou/Repr/jmaa02.pdf)
• A. D. Polyanin, A. I. Zhurov. Functional constraints method for constructing exact solutions to delay reaction-diffusion equations and more complex nonlinear equations. Communications in Nonlinear Science and Numerical Simulation, Vol. 19, No. 3, pp. 417–430, 2014. (See also: A new method for constructing exact solutions to nonlinear delay partial differential equations. arXiv:1304.5473v1 [nlin.SI] 19 Apr 2013.)
• S. V. Meleshko, S. Moyo. On the complete group classification of the reaction--diffusion equation with a delay. Journal of Mathematical Analysis and Applications, Vol. 338, pp. 448–466, 2008.
• J. Tanthanuch. Symmetry analysis of the nonhomogeneous inviscid Burgers equation with delay. Communications in Nonlinear Science and Numerical Simulation, Vol. 17, pp. 4978–4987, 2012.
• A. D. Polyanin, A. I. Zhurov. Integration of linear and some model non-linear equations of motion of incompressible fluids. International Journal of Non-Linear Mechanics, Vol. 49, pp. 77–83, 2013.
• A. D. Polyanin, A. I. Zhurov. Exact solutions of linear and non-linear differential-difference heat and diffusion equations with finite relaxation time. International Journal of Non-Linear Mechanics, Vol. 54, pp. 115–126, 2013.
• A. D. Polyanin, A. I. Zhurov. Exact solutions of non-linear differential-difference equations of a viscous fluid with finite relaxation time, International Journal of Non-Linear Mechanics. Vol. 57, p. 116–122, 2013.
• A. D. Polyanin, A. I. Zhurov. Exact separable solutions of delay reaction-diffusion equations and other nonlinear partial functional-differential equations. Communications in Nonlinear Science and Numerical Simulation, Vol. 19, No. 3, pp. 409–416, 2014.
• A. D. Polyanin, A. I. Zhurov. New generalized and functional separable solutions to non-linear delay reaction-diffusion equations. International Journal of Non-Linear Mechanics, Vol. 59, pp. 16–22, 2014.
• A. D. Polyanin, A. I. Zhurov. Generalized and functional separable solutions to nonlinear delay Klein–Gordon equations. Communications in Nonlinear Science and Numerical Simulation, Vol. 19, No. 8, pp. 2676–2689, 2014.
• A. D. Polyanin, A. I. Zhurov. Non-linear instability and exact solutions to some delay reaction-diffusion systems. International Journal of Non-Linear Mechanics, Vol. 62, pp. 33–40, 2014.
• A. D. Polyanin, A. I. Zhurov. Nonlinear delay reaction-diffusion equations with varying transfer coefficients: Exact methods and new solutions, Applied Mathematics Letters, Vol. 37, pp. 43–48, 2014.
• A. D. Polyanin, A. I. Zhurov. The functional constraints method: Application to non-linear delay reaction-diffusion equations with varying transfer coefficients, International Journal of Non-Linear Mechanics, Vol. 67, pp. 267–277, 2014.
• A. D. Polyanin, A. I. Zhurov. The generating equations method: Constructing exact solutions to delay reaction-diffusion systems and other non-linear coupled delay PDEs, International Journal of Non-Linear Mechanics, Vol. 71, pp. 104–115, 2015.
• A. D. Polyanin, V. G. Sorokin. Nonlinear delay reaction-diffusion equations: Traveling-wave solutions in elementary functions, Applied Mathematics Letters, Vol. 46, pp. 38–43, 2015.

See also:

• B. Zubik-Kowal. Delay partial differential equations. Scholarpedia, 3(4):2851, 2008.
• P. M. Jordan, W. Dai, R.E. Mickens. A note on the delayed heat equation: Instability with respect to initial data. Mechanics Research Communications, 2008, Vol. 35, pp. 414-420.
• R.  S. Ismagilov, N.  A. Rautian, V. V. Vlasov. Examples of very unstable linear partial functional differential equations. arXiv: arXiv:1402.4107 [math.AP] 17 Feb 2014.
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