Stable blow-up patterns

Alberto Bressan

doi:10.1016/0022-0396(92)90104-U

Stable blow-up patterns

Alberto Bressan

Research output: Contribution to journal › Article › peer-review

45 Scopus citations

Abstract

For the semilinear heat equation u_t = Δu + e^u in a convex domain Ω ⊂ Rⁿ, given any b ε{lunate} Ω we show the existence of solutions which blow up in finite time exactly at b and whose final profile has the form u(T, x) ≈ -2 ln |x - b| + ln |ln |x - b|| + ln 8, 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.

Original language	English (US)
Pages (from-to)	57-75
Number of pages	19
Journal	Journal of Differential Equations
Volume	98
Issue number	1
DOIs	https://doi.org/10.1016/0022-0396(92)90104-U
State	Published - Jul 1992

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Access to Document

10.1016/0022-0396(92)90104-U

Cite this

@article{266671d7bea04b83b03687ac12d27eb0,

title = "Stable blow-up patterns",

abstract = "For the semilinear heat equation ut = Δu + eu in a convex domain Ω ⊂ Rn, given any b ε\{lunate\} Ω we show the existence of solutions which blow up in finite time exactly at b and whose final profile has the form u(T, x) ≈ -2 ln |x - b| + ln |ln |x - b|| + ln 8, 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.",

author = "Alberto Bressan",

year = "1992",

month = jul,

doi = "10.1016/0022-0396(92)90104-U",

language = "English (US)",

volume = "98",

pages = "57--75",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Stable blow-up patterns

AU - Bressan, Alberto

PY - 1992/7

Y1 - 1992/7

N2 - For the semilinear heat equation ut = Δu + eu in a convex domain Ω ⊂ Rn, given any b ε{lunate} Ω we show the existence of solutions which blow up in finite time exactly at b and whose final profile has the form u(T, x) ≈ -2 ln |x - b| + ln |ln |x - b|| + ln 8, 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.

AB - For the semilinear heat equation ut = Δu + eu in a convex domain Ω ⊂ Rn, given any b ε{lunate} Ω we show the existence of solutions which blow up in finite time exactly at b and whose final profile has the form u(T, x) ≈ -2 ln |x - b| + ln |ln |x - b|| + ln 8, 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.

UR - https://www.scopus.com/pages/publications/0001908831

UR - https://www.scopus.com/pages/publications/0001908831#tab=citedBy

U2 - 10.1016/0022-0396(92)90104-U

DO - 10.1016/0022-0396(92)90104-U

M3 - Article

AN - SCOPUS:0001908831

SN - 0022-0396

VL - 98

SP - 57

EP - 75

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

Stable blow-up patterns

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this