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.File in questo prodotto:
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