Publication: Sufficient and necessary initial mass conditions for the existence of a waiting time in nonlinear-convection processes
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We study the initial behavior of the fronts (for interfaces) generated by the solutions of the equation ut=(um)xx+b(uλ)x, where m,b,λ>0 are real numbers. We derive a mass comparison principle that allows us to give necessary and sufficient conditions in order to have waiting time at the fronts. Different regions in the (λ,m) parameter space must be introduced, leading to answers of a very different nature
L. ALVAREZ. J. I. DIAZ. AND R. KERSNER. On the initial growth of the interfaces in nonlinear diffusion-convection processes, in "Nonlinear Diffusion Equations and Their Equilibrium States I” (Ni. Peletier. and Serrin. Eds.). pp. 1-20. Springer-Verlag, NewYork/Berlin. 1987. J. BEAR. "Dynamics of Fluids in Porous Media." American Elsevier, New York, 1972. J. BUCKMASTER. Viscous sheets advancing over dry bed, J. Fluid. Mech. 81 (1977.735-756. S. CHANDRASEKHAR Stochastic problems in physics and astronomy, Rev. Modern Phys. 15(1943), 1-8R9. J.I. DIAZ. AND R. KERSNER, On a nonlincar degenerate parabolic equation in infiltration or evaparatian, J. Differntial Equations 69 (1987). 368-403. J.I. DIAZ AND R. KERSNER. Non existence d’une des frontieres libres dans une equation dégénérée en theorie de la filtration. C. R. Acad. Sci. Patis 296 (1983), 505-508. J. I. DIAZ AND R. KERSNER. On the behavior and cases of nonexistence of the free boundary in a semibounded porous medium, .J. Math. Anal. Appl. 132 (1988),281-289. A. FRIEDMAN, "Partial Differential Equations of the Parabolic Type," Prentice-HalL Englewood Cliffs, NJ, 1969. B. H. GILDING, Properties of solutions of an equation in the theory of infiltration, Arch.Rational Mech. Anal. 65 (1977),203-225. B.H. GILDING, "The Occurrence of Interfaces in Nonlinear Diffusion-Advection Processes," Memorandum 595, Department of Applied Mathematics, Twente University of Technology, 1986. B. H. GILDING, "Improved Theory for a Nonlinear Degenerate Parabolic Equation,"Memorandum 587, Department of Applied Mathemalies, Twente University of Technology, 1986. B. F. KNERR, The porous medium equation in one dimension, Trans. Amer. Math. Soc.234 (1977), 381-415. O. LADYZHENSKAYA, V. SOLONNIKOV, AND URAL'CEVA, "Linear and Quasilinear Equationsof Parabolic Type," translation of Math. Monograph, Vol. 23, Amer. Math. Soc.,Providenee, RI, 1968, O. OLEINIK, A, KALASHNIKOV, ANO YUI-LIN, The Cauchy problem and boundary valueproblems for equations of the type of nonstationary filtration, Izv. Akad. Nauk. SSSR. Ser.Mat. 22 (1958), 667-704. P. ROSENAU AND S. KAMIN, Thermal waves in an absorbing and convective medium,Physica D 8 (1963), 273-283. J. L. VÁZQUEZ, The interface of one-dimensional flows in porous media, Trans. Amer.Math. Soc. 286 (1984), 787-802. J. L. VÁZQUEZ, Asymptotic behaviour and propagation properties of the one-dimensional flow of gas in porous medium, Trans. Amer. Math. Soc. 277 (1983), 507-527.