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2011 | 9 | 3 | 673-685
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The finite speed of propagation of solutions of the Neumann problem of a degenerate parabolic equation

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In this paper the finite speed of propagation of solutions and the continuous dependence on the nonlinearity of a degenerate parabolic partial differential equation are discussed. Our objective is to derive an explicit expression for the speed of propagation and the large time behavior of the solution and to show that the solution continuously depends on the nonlinearity of the equation.
  • Jimei University
  • [1] Adams R.A., Sobolev Spaces, Pure Appl. Math., 65, Academic Press, New York-London, 1975
  • [2] Alikakos N.D., L p bounds of solutions of reaction-diffusion equations, Comm. Partial Differential Equations, 1979, 4(8), 827–868
  • [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
  • [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
  • [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)
  • [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
  • [7] Cockburn B., Gripenberg G., Continuous dependence on the nonlinearities of solutions of degenerate parabolic equations, J. Differential Equations, 1999, 151(2), 231–251
  • [8] Gilding B.H., Properties of solutions of an equation in the theory of infiltration, Arch. Rational Mech. Anal., 1977, 65(3), 203–225
  • [9] Gilding B. H., The occurrence of interfaces in nonlinear diffusion-advection processes, Arch. Rational Mech. Anal., 1988, 100(3), 243–263
  • [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] 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
  • [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] Schonbek M.E., Asymptotic behavior of solutions to viscous conservation laws with slowly varying external forces, Math. Ann., 2006, 336(3), 505–538
  • [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] Wu Z., Yin J., Wang C., Introduction to Partial Differential Equations of Elliptic and Parabolic Type, Science Press, Beijing, 2004 (in Chinese)
  • [16] Yau S.-T., Differential Geometry, Scientific Press, Beijing, 1988 (in Chinese)
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