The finite speed of propagation of solutions of the Neumann problem of a degenerate parabolic equation

 Access to full text

 Full (PDF)

1. [1] Adams R.A., Sobolev Spaces, Pure Appl. Math., 65, Academic Press, New York-London, 1975 
2. [2] Alikakos N.D., L p bounds of solutions of reaction-diffusion equations, Comm. Partial Differential Equations, 1979, 4(8), 827–868 http://dx.doi.org/10.1080/03605307908820113 Zbl0421.35009
3. [3] Alikakos N.D., Rostamian R., Large time behavior of solutions of Neumann boundary value problem for the porous medium equation, Indiana Univ. Math. J., 1981, 30(5), 749–785 http://dx.doi.org/10.1512/iumj.1981.30.30056 Zbl0598.76100
4. [4] Aronson D.G., Bénilan Ph., Régularité des solutions de l’équation des milieux poreux dans ℝN, C. R. Acad. Sci. Paris Sér. A-B, 1979, 288(2), 103A–105A Zbl0397.35034
5. [5] Barenblatt G.I., On some unsteady motions of a liquid and gas in a porous medium, Prikl. Mat. Mekh., 1952, 16(1), 67–78 (in Russian) Zbl0049.41902
6. [6] Bénilan Ph., Crandall M.G., The continuous dependence on φ of solutions of u t − Δφ (u) = 0, Indiana Univ. Math. J., 1981, 30(2), 161–177 http://dx.doi.org/10.1512/iumj.1981.30.30014 Zbl0482.35012
7. [7] Cockburn B., Gripenberg G., Continuous dependence on the nonlinearities of solutions of degenerate parabolic equations, J. Differential Equations, 1999, 151(2), 231–251 http://dx.doi.org/10.1006/jdeq.1998.3499 
8. [8] Gilding B.H., Properties of solutions of an equation in the theory of infiltration, Arch. Rational Mech. Anal., 1977, 65(3), 203–225 http://dx.doi.org/10.1007/BF00280441 Zbl0366.76074
9. [9] Gilding B. H., The occurrence of interfaces in nonlinear diffusion-advection processes, Arch. Rational Mech. Anal., 1988, 100(3), 243–263 http://dx.doi.org/10.1007/BF00251516 Zbl0672.76094
10. [10] Ladyženskaja O.A., Solonnikov V.A., Ural’ceva N. N., Linear and Quasi-linear Equations of Parabolic Type, Transl. Math. Monogr., 23, American Mathematical Society, Providence, 1967 
11. [11] Lair A.V., Oxley M.E., A necessary and sufficient condition for global existence for a degenerate parabolic boundary value problem, J. Math. Anal. Appl., 1998, 221(1), 338–348 http://dx.doi.org/10.1006/jmaa.1997.5900 
12. [12] Peletier L.A., On the existence of an interface in nonlinear diffusion processes, In: Ordinary and Partial Differential Equations, Dundee, 26–29 March 1974, Lecture Notes in Math., 415, Springer, Berlin-New York, 1974, 412–416 
13. [13] Schonbek M.E., Asymptotic behavior of solutions to viscous conservation laws with slowly varying external forces, Math. Ann., 2006, 336(3), 505–538 http://dx.doi.org/10.1007/s00208-006-0759-2 Zbl1184.35263
14. [14] Vázquez J.L., An introduction to the mathematical theory of the porous medium equation, In: Shape Optimization and Free Boundaries, Montreal, 1990, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 380, Kluwer, Dordrecht, 1992, 347–389 
15. [15] Wu Z., Yin J., Wang C., Introduction to Partial Differential Equations of Elliptic and Parabolic Type, Science Press, Beijing, 2004 (in Chinese) 
16. [16] Yau S.-T., Differential Geometry, Scientific Press, Beijing, 1988 (in Chinese)