Single-point blowup for nonlocal parabolic problems

Physica D: Nonlinear Phenomena

Volumn 134, Issue 1, 1999, Pages 48-60

  Bebernes, J ^a   Li, C ^a   Talaga, P ^b  

^a UNIVERSITY OF COLORADO   (United States)

^b WEBER STATE UNIVERSITY   (United States)

Author keywords

Blow up; Localization; Nonlocal parabolic partial differential equations; Shear band formation; Singularities

Indexed keywords

EID: 0040357230     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00057-3     Document Type: Article

References (22)

1. Bebernes J., Bressan A. Thermal behavior for a confined reactive gas. J. Diff. Equations. 44:1982;118-133.
2. Bebernes J., Bressan A., Eberly D. A description of blow-up for the solid fuel ignition model. Indiana Math. J. 36:1987;295-305.
3. Bebernes J., Eberly D. A description of self-similar blowup for the solid fuel ignition model for dimensions. n≥3 , Analyse Non Linéaire Ann. Inst. Henri Poincarè 5(1):1988;1-21.
4. Bebernes J., Bressan A., Lacey A. Total blowup versus single point blowup. J. Diff. Equations. 73(1):1988;30-44.
5. Bebernes J., Eberly D. Characterization of blow-up for a semilinear heat equation with a convection term. Quart. J. Mech. Appl. Math. 42:1989;447-456.
6. J. Bebernes, D. Eberly, Mathematical problems from combustion theory, Appl. Math. Sci., vol. 83, Springer, Berlin, 1989.
7. Bebernes J., Bricher S. Final time blowup profiles for semilinear parabolic equations via center manifold theory. SIAM J. Math. Analysis. 23:1992;852-869.
8. Bebernes J., Bricher S., Galaktionov V. Asymptotics of blowup for weakly quasilinear parabolic problems. Nonlinear Anal. 23:1994;489-514.
9. Bebernes J., Lacey A. Global existence and finite-time blow-up for a class of nonlocal parabolic problems. Advances in Differential Equations. 2:1997;927-953.
10. Bebernes J., Talaga P. Nonlocal problems modelling shear banding. Comm. Appl. Nonlinear Analysis. 3:1996;79-103.
11. S. Bricher, E. Adkdogu, The asymptotic behavior for gaseous ignition models, J. Comp. Appl. Math. 95 (1998), in press.
12. Burns T.J. A mechanism for shear band formation in the high strain-rate torsion test. J. Appl. Mech. 57:1990;836-844.
13. T.J. Burns, On a combustion-like model for plastic strain localization, in: R. Fosdick (Ed.), Shock Induced Transitions and Phase Structures in General Media, Springer, Berlin, 1992 (Chapter 2).
14. Burns T.J. Does a shear band result from a thermal explosion? Mechanics of Materials. 17:1994;261-271.
15. T.J. Burns, Connections between localized behavior in plasticity and in combustion, in: R.C. Batra, H.M. Zbib (Eds.), Material Instabilities - Theory and Application, The American Soc. of Mech. Engineers, Book No. G00895, 1994, pp. 87-93.
16. Fila M. Boundedness of global solutions of nonlinear diffusion equations. J. Differential Equations. 98:1992;226-240.
17. M. Fila, Boundedness of global solutions of nonlocal parabolic equations, in press.
18. p Comm. Pure Appl. Math. 45:1992;821-869.
19. Friedman A., McLeod B. Blowup of positive solutions of semilinear heat equations. Indiana Univ. J. Math. 34:1985;425-477.
20. Marchand A., Duffy J. An experimental study of the formation of adiabatic shear bands in a structural steel. J. Mech. Phys. Solids. 36:1988;251-283.
21. Olmstead W.E., Nemat-Nasser S., Ni L. Shear bands as surfaces of discontinuity. J. Mech. Phys. Solids. 42:1994;697-709.
22. Walter J.W. Numerical experiments on adiabatic shear bands. Int. J. Plasticity. 8:1992;657-693.