@article{AIHPC_2002__19_5_505_0,
author = {Zaag, Hatem},
title = {On the regularity of the blow-up set for semilinear heat equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {505--542},
year = {2002},
publisher = {Elsevier},
volume = {19},
number = {5},
mrnumber = {1922468},
zbl = {1012.35039},
language = {en},
url = {https://www.numdam.org/item/AIHPC_2002__19_5_505_0/}
}
Zaag, Hatem. On the regularity of the blow-up set for semilinear heat equations. Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002) no. 5, pp. 505-542. https://www.numdam.org/item/AIHPC_2002__19_5_505_0/
[1] , Remarks on blow-up and nonexistence theorems for nonlinear evolution equations, Quart. J. Math. Oxford (Ser. 2) 28 (112) (1977) 473-486. | Zbl | MR
[2] , , , Axisymmetric surface diffusion: dynamics and stability of self-similar pinchoff, J. Statist. Phys. 93 (3-4) (1998) 725-776. | Zbl | MR
[3] M.D. Betterton, M.P. Brenner, Collapsing bacterial cylinders, Preprint.
[4] , , , , , Diffusion, attraction and collapse, Nonlinearity 12 (4) (1999) 1071-1098. | Zbl | MR
[5] , , Universality in blow-up for nonlinear heat equations, Nonlinearity 7 (2) (1994) 539-575. | Zbl | MR
[6] , , , Vortices and boundaries, Quart. Appl. Math. 56 (3) (1998) 507-519. | Zbl | MR
[7] , , The role of critical exponents in blow-up theorems: the sequel, J. Math. Anal. Appl. (2000). | Zbl | MR
[8] , , , Stability of the blow-up profile of non-linear heat equations from the dynamical system point of view, Math. Annalen 317 (2) (2000) 195-237. | Zbl | MR
[9] , , Boundedness up to blow-up of the difference between two solutions to a semilinear heat equation, Nonlinearity 13 (4) (2000) 1189-1216. | Zbl | MR
[10] , , Refined asymptotics for the blowup of ut−Δu=up, Comm. Pure Appl. Math. 45 (7) (1992) 821-869. | Zbl
[11] , , On the blowup of multidimensional semilinear heat equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (3) (1993) 313-344. | Zbl | MR | Numdam
[12] , 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. | Zbl
[13] , , Nondegeneracy of blowup for semilinear heat equations, Comm. Pure Appl. Math. 42 (6) (1989) 845-884. | Zbl | MR
[14] , , Blow-up behaviour of one-dimensional semilinear parabolic equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (2) (1993) 131-189. | Zbl | MR | Numdam
[15] , Perturbation Theory for Linear Operators, Springer, Berlin, 1995, Reprint of the 1980 edition. | Zbl | MR
[16] , Some nonexistence and instability theorems for solutions of formally parabolic equations of the form Put=−Au+F(u), Arch. Rational Mech. Anal. 51 (1973) 371-386. | Zbl
[17] , Solution of a nonlinear heat equation with arbitrarily given blow-up points, Comm. Pure Appl. Math. 45 (3) (1992) 263-300. | Zbl | MR
[18] , , Reconnection of vortex with the boundary and finite time quenching, Nonlinearity 10 (6) (1997) 1497-1550. | Zbl | MR
[19] , , Stability of the blow-up profile for equations of the type ut=Δu+|u|p−1u, Duke Math. J. 86 (1) (1997) 143-195. | Zbl
[20] , , Optimal estimates for blowup rate and behavior for nonlinear heat equations, Comm. Pure Appl. Math. 51 (2) (1998) 139-196. | Zbl | MR
[21] , , A Liouville theorem for vector-valued nonlinear heat equations and applications, Math. Annalen 316 (1) (2000) 103-137. | Zbl | MR
[22] F. Oustry, M.L. Overton, Variational analysis of the total projection for symmetric matrices, 2000.
[23] , , Singularities and uniqueness of cylindrically symmetric surfaces moving by mean curvature, Comm. Partial Differential Equations 18 (5-6) (1993) 859-894. | Zbl | MR
[24] , Higher-dimensional blow up for semilinear parabolic equations, Comm. Partial Differential Equations 17 (9-10) (1992) 1567-1596. | Zbl | MR
[25] , Classification of singularities for blowing up solutions in higher dimensions, Trans. Amer. Math. Soc. 338 (1) (1993) 441-464. | Zbl | MR
[26] , Estimates on the (n−1)-dimensional Hausdorff measure of the blow-up set for a semilinear heat equation, Indiana Univ. Math. J. 42 (2) (1993) 445-476. | Zbl
[27] H. Zaag, One-dimensional behavior of singular N-dimensional solutions of semilinear heat equations, Preprint, 2001. | MR






