Propagation of perturbations in quasilinear multidimensional parabolic equations with convective term

Ukrainian Mathematical Journal

Volumn 53, Issue 7, 2001, Pages 1134-1155

  Sapronov, D A ^a   Shishkov, A E ^a  

^a INSTITUTE OF APPLIED MATHEMATICS AND MECHANICS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646398240     PISSN: 00415995     EISSN: 15739376     Source Type: Journal    
DOI: 10.1023/A:1013381316300     Document Type: Article

References (14)

1. A. S. Kalashnikov, "On some problems in the qualitative theory of nonlinear second-order degenerating parabolic equations," Usp. Mat. Nauk., 42, No. 2, 135-176 (1987).
2. B. H. Gilding and L. A. Peletier, "The Cauchy problem for an equation in theory of infiltration," Arch. Ration. Mech. Anal., 61, 127-140 (1976).
3. B. H. Gilding, "Properties of solutions of an equation in the theory of infiltration," Arch. Ration. Mech. Anal., 65, 203-225 (1977).
4. R. E. Grundy, "Asymptotic solution of a model nonlinear convective diffusion equation," IMA J. Appl. Math., 31, 121-137 (1983).
5. L. Alvarez, J. I. Diaz, and R. Kersner, "On the initial growth of the interfaces in nonlinear diffusion-convection processes," in: W.-M. Ni, L. A. Peletier, and J. Serrin (editors), Nonlinear Diffusion Equations and Their Equilibrium States. I, Springer, New York (1987), pp. 1-20.
6. L. Alvarez and J. I. Diaz, "Sufficient and necessary initial mass conditions for the existence of a waiting time in nonlinear-convection processes," J. Math. Anal. Appl., 155, 378-393 (1991).
7. J. I. Diaz and R. Kersner, "Non existence d'une des frontieres libres dans une equation degeneree en théorie de la filtration," C. R. Acad. Sel, 296, 505-508 (1983).
8. B. H. Gilding, The Occurrence of Interfaces in Nonlinear Diffusion-Advection Processes, Memorandum 595, Dep. Appl. Math., Twente University of Technology (1986).
9. B. H. Gilding and A. E. Shishkov, The Effect of a Convection Term on the Propagation Properties of a Nonlinear Parabolic Equation, Preprint, Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk (1998).
10. H. Alt and S. Luckhaus, "Quasilinear elliptic-parabolic differential equations," Math. Z., 183,311-341(1983).
11. P. Benilan and O. Wittbold, "On mild and weak solutions of elliptic-parabolic problems," Adv. Different. Equal., 1, 1053-1073 (1996).
12. F. Bernis, "Existence results for doubly nonlinear higher order parabolic equations on unbounded domains," Math., 279, 373-394(1988).
13. F. Bernis, "Qualitative properties for some nonlinear higher order degenerate parabolic equations," Math., 14, No. 3, 319-352 (1988).
14. A. E. Shishkov, "Propagation of perturbations in a singular Cauchy problem for quasilinear degenerating parabolic equations," Mat. Sb., 187, No. 9, 139-160 (1996).