Generic behaviour of one-dimensional blow up patterns

 Access to full text

 Full (PDF)

1. [B1] A. Bressan, On the asymptotic shape of blow up, Indiana Univ. Math. J., 39, 4 (1990), 947-960. Zbl0705.35014MR1087180
2. [B2] A. Bressan, Stable blow up patterns, J. Differential Equations, 98 (1992), 57-75. Zbl0770.35010MR1168971
3. [BE] J. Bebernes - D. Eberly, Mathematical problems from combustion theory, Appl. Math. Sci.83, Springer (1989). Zbl0692.35001MR1012946
4. [CM] X.Y. Chen - H. Matano, Convergence, asymptotic periodicity and finite point blow up in one-dimensional semilinear heat equations, J. Differential Equations, 78 (1989), 160-190. Zbl0692.35013MR986159
5. [D] J.W. Dold, Analysis of the early stage of thermal runaway, Quart. J. Mech. Appl. Math.38 (1985), 361-387. Zbl0569.76079
6. [F] A. Friedman, Partial Differential Equations of parabolic type, Robert E. Krieger Co (1983). 
7. [FK] S. Filippas - R.V. Kohn, Refined asymptotics for the blow up of u t - Δu = up, Comm. Pure. Appl. Math., XLV (1992), 821-869. Zbl0784.35010
8. [FM] A. Friedman - J.B. Mcleod, Blow up of positive solutions of semilinear heat equations, Indiana Univ. Math. J., 34 (1985), 425-447. Zbl0576.35068MR783924
9. [Fu] H. Fujita, On the blowing up of solutions of the Cauchy problem for ut = Δu+u1+α, J. Fac. Sci. Univ. Tokyo Sect. I, 13 (1966), 109-124. Zbl0163.34002
10. [GHV] V.A. Galaktionov - M.A. Herrero - J.J.L. Velázquez, The space structure near a blow up point for semilinear heat equations, Soviet J. Comput. Math. and Math. Physics, 31 (1991), 399-411. Zbl0747.35014MR1107061
11. [GK1] Y. Giga - R.V. Kohn, Asymptotically self-similar blow up of semilinear heat equations, Comm. Pure Appl. Math., 38 (1985), 297-319. Zbl0585.35051MR784476
12. [GK2] Y. Giga - R.V. Kohn, Characterizing blow up using similarity variables, Indiana Univ. Math. J., 36 (1987), 1-40. Zbl0601.35052MR876989
13. [GK3] Y. Giga - R.V. Kohn, Nondegeneracy of blow up for semilinear heat equations, Comm. Pure Appl. Math., 42 (1989), 845-884. Zbl0703.35020MR1003437
14. [GP] V.A. Galaktionov - S.A. Posashkov, Application of new comparison theorems in the investigation of unbounded solutions of nonlinear parabolic equations, Differential Equations, 22, 7 (1986), 116-1183. Zbl0632.35028MR853803
15. [HV1] M.A. Herrero - J.J.L. Velázquez, Blow up behaviour of one-dimensional semilinear parabolic equations, Ann. Inst. H. Poincaré, to appear. Zbl0813.35007MR1220032
16. [HV2] M.A. Herrero - J.J.L. Velázquez, Flat blow up in one-dimensional semilinear heat equations, Differential Integral Equations, Vol. 5, n° 5 (1992), 973-997. Zbl0767.35036MR1171974
17. [HV3] M.A. Herrero - J.J.L. Velázquez, Blow up profiles in one-dimensional, semilinear parabolic problems, Comm. Partial Differential Equations, 17, 182, (1992), 205-219. Zbl0772.35027MR1151261
18. [HV4] M.A. Herrero - J.J.L. Velázquez, Plane structures in thermal runaway, Israel J. Math., to appear. Zbl0813.35035MR1231197
19. [HSS] L.M. Hocking - K. Stewartson - J.T. Stuart, A nonlinear instability burst in plane parallel flow, J. Fluid Mech. J1 (1972), 705-735. Zbl0232.76053
20. [LM] J.L. Lions - B. Malgrange, Sur l'unicité retrograde, Math. Scand.8 (1960), 277-286. Zbl0126.12202MR140855
21. [M] F. Merle, Solution of a nonlinear heat equation with arbitrarily given blow up points, Comm. Pure. Appl. Math., to appear. Zbl0785.35012MR1151268
22. [MW] C.E. Müller - F.B. Weissler, Single point blow up for a general semilinear heat equation, Indiana Univ. Math. J., 34 (1983), 881-913. Zbl0597.35057MR808833
23. [V] J.J.L. Velázquez, Local behaviour near blow up points for semilinear parabolic equations, J. Differential Equations, to appear. Zbl0798.35023MR1251859
24. [W] F.B. Weissler, Single point blow up of semilinear initial value problems, J. Differential Equations, 55 (1984), 204-224. Zbl0555.35061MR764124

1. Philippe Souplet, Blow-up behavior in nonlocal vs local heat equations
2. Alberto Bressan, Sistemi iperbolici di leggi di conservazione
3. Théodore Boni, Firmin N'Gohisse, Continuity of the quenching time in a semilinear parabolic equation
4. J. J. L. Velázquez, Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow