Asymptotic behaviour of solutions of some semilinear parabolic problems

 Access to full text

 Full (PDF)

1. [1] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions. Dover Pub. Inc., 1970. 
2. [2] H. Brezis, Semilinear equations in RN without conditions at infinity. Appl. Math. Optim., Vol. 12, 1984, pp. 271-282. Zbl0562.35035MR768633
3. [3] H. Brezis and A. Friedman, Nonlinear parabolic equations involving measures as initial conditions. Journal de Mathématiques Pures et Appliquées, Vol. 62, 1983, pp. 73-97. Zbl0527.35043MR700049
4. [4] C.M. Bender and S.A. Orszag, Advanced mathematical methods for scientists and engineers. McGraw-Hill Inc., 1978. Zbl0417.34001MR538168
5. [5] H. Brezis, L.A. Peletier and D. Terman, A very singular solution of the heat equation with absorption. Arch. Rat. Mech. Anal., Vol. 95, 1986, pp. 185-209. Zbl0627.35046MR853963
6. [6] M. Escobedo and O. Kavian, Variational problems related to self-similar solutions of the heat equation. Nonlinear Analysis T. M. A., Vol. 11, 1987, pp. 1103-1133. Zbl0639.35038MR913672
7. [7] M. Escobedo, O. Kavian and H. Matano, Large time behavior of solutions of a dissipative semilinear heat equation. Comm. in PDE, Vol. 20, 1995, pp. 1427-1452. Zbl0838.35015MR1335757
8. [8] A. Friedman, Partial differential equations of parabolic type. Robert E. Krieger Pub. Co, 1983. MR454266
9. [9] Y. Giga and R.V. Kohn, Asymptotically self-similar blow-up of semilinear heat equations. Comm. Pure Appl. Math., Vol. 38, 1985, pp. 287-319. Zbl0585.35051MR784476
10. [10] V.A. Galaktionov, S.P. Kurdyumov and A.A. Samarskii, On asymptotic "eigenfunctions" of the Cauchy problem for a nonlinear parabolic equation. Math. USSR Sbornik, Vol. 54, 1986, pp. 421-455. Zbl0607.35049MR788082
11. [11] A. Galindo and P. Pascual, Quantum Mechanics., Springer Verlag, 1991. Zbl0824.00009
12. [12] A. Gmira and L. Veron, Large time behaviour of the solutions of a semilinear parabolic equation in RN. Journal of Differential Equations, Vol. 53, 1984, pp. 258-276. Zbl0529.35041MR748242
13. [13] M.A. Herrero and J.J.L. Velazquez, Blow-up behaviour of one-dimensional semilinear parabolic equations. Ann. Inst. Henri Poincaré, Vol. 10, 2, 1993, pp. 131-189. Zbl0813.35007MR1220032
14. [14] S. Kamin and L.A. Peletier, Large time behaviour of solutions of the heat equation with absorption. Annali Scuola Normale Sup. di Pisa, Vol. XII, 3, 1985, pp. 393-408. Zbl0598.35050MR837255
15. [15] S. Kamin and M. Ughi, On the behaviour as t → ∞ of the solutions of the Cauchy problem for certain nonlinear parabolic equations. Journal of Mathematical Analysis and Applications, Vol. 128, 1987, pp. 456-469. Zbl0643.35048MR917378
16. [16] J.J.L. Velazquez, Classification of singularities for blowing up solutions in higher dimensions. Trans. of the A. M. S., Vol. 338, 1, 1993, pp. 441-464. Zbl0803.35015MR1134760

1. Thierry Cazenave, Flávio Dickstein, Fred B. Weissler, Universal solutions of a nonlinear heat equation on ${ℝ}^N$
2. Piotr Biler, Grzegorz Karch, A Neumann problem for a convection-diffusion equation on the half-line
3. Vladimir Varlamov, Nonlinear Heat Equation with a Fractional Laplacian in a Disk
4. Vladimir Varlamov, Long-time asymptotics for the nonlinear heat equation with a fractional Laplacian in a ball