For the semilinear heat equation ut = Δu + eu in a convex domain Ω ⊂ n, given any we show the existence of solutions which blow up in finite time exactly at b and whose final profile has the form T being the blow-up time. Using a suitable set of rescaled coordinates, this asymptotic behavior is proved to be stable with respect to small perturbations of the initial conditions.

Stable blow-up patterns / Bressan, Alberto. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 98:1(1992), pp. 57-75. [10.1016/0022-0396(92)90104-U]

Stable blow-up patterns

Bressan, Alberto
1992-01-01

Abstract

For the semilinear heat equation ut = Δu + eu in a convex domain Ω ⊂ n, given any we show the existence of solutions which blow up in finite time exactly at b and whose final profile has the form T being the blow-up time. Using a suitable set of rescaled coordinates, this asymptotic behavior is proved to be stable with respect to small perturbations of the initial conditions.
1992
98
1
57
75
Bressan, Alberto
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/30506
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 45
  • ???jsp.display-item.citation.isi??? 39
social impact