Boundary value problems for strongly degenerate parabolic equations

Communications in Partial Differential Equations

Volumn 22, Issue 1-2, 1997, Pages 17-38

  Lavientiev Jr , M ^a   Broadbridge, P ^b   Belov, V ^b  

^a ENERGY SYSTEMS INSTITUTE   (Russian Federation)

^b UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038967499     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309708821253     Document Type: Article

References (17)

1. D.D. Joseph and L. Preziosi, Heat waves, Rev. Mod. Phys., 61 (1989), 41-73.
2. J.R. Philip, General, method of exact solution of the concentration -dependent diffusion equation, Aust. J. Phys., 13 (1960), 1-12.
3. J.J. Meyer and A.W. Warrick, Analytical expressions for soil water diffusivity derived from horizontal infiltration experiments, Soil Sci. Soc. Am. J. 54 (1990), 1547-1552.
4. P. Broadbridge, P. Tritscher, and A. Avagliano, Free boundary problems with nonlinear diffusion, Math. Comput. Modelling, 18 (1993), 15-34.
5. P. Rosenau, Free-energy functionals at the high-gradient limit, Phys. Rev., A 41 (1990), 2227-2230.
6. W. W. Mullins, Theory of thermal grooving, J. Appl. Phys., 28 (1951), 333-339.
7. P. Broadbridge, Exact solvability of the Mullins nonlinear diffusion model of groove development, J. Math. Phys., 30 (1989), 1648-1651.
8. G.I. Barenblatt, M. Bertsch, R. Dal Passo and M. Ughi, A degenerate pseudoparabolic regularization of a nonlinear forward-backward heat equation arising in the theory of heat and mass exchange in stably stratified turbulent shear flow, SIAM J. Math. Anal., 24 (1993), no. 6, 1414-1439.
9. G.I. Barenblatt, M. Bertsch, R. Dal Passo, V. Prostokishin and M. Ughi, A mathematical model of turbulent heat, and mass transfer in stably stratified turbulent shear flow, J. Fluid Mech., 253 (1993), 341-358.
10. K. Höllig, Existence of infinitely many solutions for a forward-backward heat equation, Trans. Amer. Math. Soc., 278 (1983), no. 1, 299-316.
11. M. Bertsch, R. Dal Passo, Hyperbolic phenomena in strongly degenerate parabolic equation, Arch. Rational Mech. Anal., 117 (1992), 349-387.
12. M. Fila and G. Lieberman, Derivative blow-up and beyond for quasilinear parabolic equations, Diff. and Integral Equations, 7 (1994), no. 3/4, 811-822.
13. M.P. Vishnevsky, T.I. Zelenyak and M.M. Lavrentiev Jr., Behaviour of solutions to parabolic equations for large time, Sib. Mat. Zhurn., 36 (1995), no. 3, 510-530. (Russian)
14. S. Angenent and M. Fila, Interior gradient blow-up in a semilinear parabolic equation. (To appear)
15. O.A. Ladyžhenskaya, V.S. Solonnikov and N.N. Ural'tseva, Linear and quasilinear equations of parabolic type, Amer Math. Soc., Providence, Rhode Island, 1968.
16. S.N. Kruzhkov, Quasilinear parabolic equations and systems with two independent variables, Proceedings of I.G. Petrovsky seminar, 5 (1979), 217-272. (Russian)
17. V.S. Belonosov and T.I. Zelenyak, Nonlocal problems in theory of quasilinear parabolic equations, Novosibirsk State University, Novosibirsk, 1975. (Russian)