@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}, publisher = {Elsevier}, volume = {19}, number = {5}, year = {2002}, mrnumber = {1922468}, zbl = {1012.35039}, language = {en}, url = {http://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. http://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. | MR | Zbl
,[2] Axisymmetric surface diffusion: dynamics and stability of self-similar pinchoff, J. Statist. Phys. 93 (3-4) (1998) 725-776. | MR | Zbl
, , ,[3] M.D. Betterton, M.P. Brenner, Collapsing bacterial cylinders, Preprint.
[4] Diffusion, attraction and collapse, Nonlinearity 12 (4) (1999) 1071-1098. | MR | Zbl
, , , , ,[5] Universality in blow-up for nonlinear heat equations, Nonlinearity 7 (2) (1994) 539-575. | MR | Zbl
, ,[6] Vortices and boundaries, Quart. Appl. Math. 56 (3) (1998) 507-519. | MR | Zbl
, , ,[7] The role of critical exponents in blow-up theorems: the sequel, J. Math. Anal. Appl. (2000). | MR | Zbl
, ,[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. | MR | Zbl
, , ,[9] Boundedness up to blow-up of the difference between two solutions to a semilinear heat equation, Nonlinearity 13 (4) (2000) 1189-1216. | MR | Zbl
, ,[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. | Numdam | MR | Zbl
, ,[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. | MR | Zbl
, ,[14] Blow-up behaviour of one-dimensional semilinear parabolic equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (2) (1993) 131-189. | Numdam | MR | Zbl
, ,[15] Perturbation Theory for Linear Operators, Springer, Berlin, 1995, Reprint of the 1980 edition. | MR | Zbl
,[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. | MR | Zbl
,[18] Reconnection of vortex with the boundary and finite time quenching, Nonlinearity 10 (6) (1997) 1497-1550. | MR | Zbl
, ,[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. | MR | Zbl
, ,[21] A Liouville theorem for vector-valued nonlinear heat equations and applications, Math. Annalen 316 (1) (2000) 103-137. | MR | Zbl
, ,[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. | MR | Zbl
, ,[24] Higher-dimensional blow up for semilinear parabolic equations, Comm. Partial Differential Equations 17 (9-10) (1992) 1567-1596. | MR | Zbl
,[25] Classification of singularities for blowing up solutions in higher dimensions, Trans. Amer. Math. Soc. 338 (1) (1993) 441-464. | MR | Zbl
,[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