Local and non-local boundary quenching

Mathematical Methods in the Applied Sciences

Volumn 22, Issue 16, 1999, Pages 1465-1484

  Roberts, Catherine A ^a   Olmstead, W E ^b  

^a NORTHERN ARIZONA UNIVERSITY   (United States)

^b Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; GREEN'S FUNCTION; INTEGRAL EQUATIONS; INTEGRATION; PROBLEM SOLVING;

BOUNDARY QUENCHING; NONLINEAR BOUNDARY CONDITION; ONE DIMENSIONAL HEAT EQUATION; PARABOLIC EQUATIONS; VOLTERRA INTEGRAL EQUATIONS;

QUENCHING;

EID: 0033228312     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1476(19991110)22:16<1465::AID-MMA88>3.0.CO;2-#     Document Type: Article

References (10)

1. Bleistein, N. and Handelsman, R. A., Asymptotic Expansion of Integrals Holt, Rinehardt and Winston, New York, 1975.
2. Deng, K. and Roberts, C. A., 'Quenching for a diffusive equation with a concentrated singularity, Differential Integral Equations, 10, 369-379 (1997).
3. Fila, M. and Levine, H. A., 'Quenching on the Boundary', Nonlinear Anal. Meth. Appl., 21, 795-802 (1993).
4. Levine, H. A., 'The phenomenon of quenching: a survey', in: Proc. 6th Int. Conf. on Trends in Theory and Practice of Nonlinear Anal., (Lakshmikantham, ed.), North-Holland, New York, 1985, pp. 275-286.
5. Levine, H. A., 'Advances in quenching', in: Progress in Nonlinear Differential Equations: Proc. Int. Conf. on Reaction-Diffusion Eqns and their Equilibrium States, (Lloyd, Ni, Peletier, Serrin, eds.), Birkhäuser, Boston, 1988, pp. 319-346.
6. Levine, H. Z., 'Quenching and beyond: a survey of recent results', Gakuto Int. Ser. Math. Sci. and Appl., 2, 501-512 (1993).
7. Olmstead, W. E. and Roberts, C. A., 'Explosion in a diffusive strip due to a concentrated nonlinear source', Meth. Appl. Anal., 1, 434-445 (1994).
8. Olmstead, W. E. and Roberts, C. A., 'Quenching for the heat equation with a nonlocal nonlinearity', in: Nonlinear Problems in Applied Mathematics, (Angell, Cook, Kleinman and Olmstead, eds.), SIAM, Philadelphia, 1995, pp. 199-205.
9. Roberts, C. A., Lasseigne, D. G. and Olmstead, W. E., 'Volterra equations which model explosion in a diffusive medium', J. Integral Equations Appl., 5, 531-545 (1993).
10. Roberts, C. A. and Olmstead, W. E., 'Growth rates for blow-up solutions of nonlinear Volterra equations', Quart. Appl. Math., 54, 153-159 (1996).