References
- Barenblatt, G.I. “On some unsteady motions of a liquid or a gas in a porous medium.” Prikl. Mat. Mekh. 16 (1952): 67-78. Cited on 54.
- Basti, B., and N. Benhamidouche. “Global existence and blow-up of generalized self-similar solutions to nonlinear degenerate diffusion equation not in divergence form.” Appl. Math. E-Notes 20 (2020): 367-387. Cited on 54 and 55.
- Benhamidouche, N. “Exact solutions to some nonlinear PDEs, traveling profiles method.” Electron. J. Qual. Theory Differ. Equ. 15 (2008): 1-7. Cited on 54 and 55.
- Benhamidouche, N., and Y. Arioua. “New method for constructing exact solutions to non-linear PDEs.” Int. J. Nonlinear Sci. 7 (2009): 395-398. Cited on 55.
- Caffarelli, L., and J.L. Vàzquez. “Viscosity solutions for the porous medium equation.” Proc. Sympos. Pure Math. 65 (1999): 13-26. Cited on 54.
- Gilding, B.E., and L.A. Peletier. “On a class of similarity solution of the porous medium equation I.” J. Math. Anal. Appl. 55 (1976): 351-364. Cited on 54 and 55.
- Granas, A., and J. Dugundji. Fixed Point Theory. New York: Springer-Verlag, 2003. Cited on 65 and 68.
- Guo, D., and V. Lakshmikantham. Nonlinear Problems in Abstract Cones. New York: Academic Press, 1988. Cited on 68.
- Hulshof, J., and J.L. Vàzquez. “Self-similar solutions of the second kind for the modified porous medium equation.” Eur. J. Appl. Math. 5 (1994): 391-403. Cited on 54.
- Hulshof, J., and J.L. Vàzquez. “Maximal viscosity solutions of the modified porous medium equation and their asymptotic behavior.” Eur. J. Appl. Math. 7 (1996): 453-471. Cited on 54.
- Ibragimov, N.H. CRC Handbook of Lie Group Analysis of Differential Equations. Vol.1: Symmetries, Exact Solutions and Conservation Laws. Boca Raton: CRC Press, 1994. Cited on 54.
- Olver, P.J. Applications of Lie Groups to Differential Equations. New York: Springer-Verlag, 1986. Cited on 54.
- Polyanin, A.D., and V.F. Zaitsev. Handbook of Nonlinear Partial Differential Equations. Boca Raton: Chapman & Hall/CRC, 2004. Cited on 54 and 55.
- Vàzquez, J.L. The Porous Medium Equation: Mathematical Theory. Oxford: Oxford University Press, 2007. Cited on 54.
- Wang, C., and Jingxue. “Shrinking self-similar solution of a nonlinear diffusion equation with nondivergence form.” J. Math. Anal. Appl. 289 (2004): 387-404. Cited on 54.