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Stable determination of a semilinear term in a parabolic equation
Multiple bubbling for the exponential nonlinearity in the slightly supercritical case
| 1. | Departamento de Ingeneria Matematica F.C.F.M., Casilla 170 Correro 3, Santiago, Chile |
| 2. | Ceremade (UMR CNRS no. 7534), Université Paris Dauphine, Place de Lattre de Tassigny, 75775 Paris Cédex 16 |
| 3. | Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino |
$ -\Delta_{2-\varepsilon} u=\lambdae^u$ in $B\quad u =0 $ on $ \partial B,$
for small $\varepsilon>0$. We show that if $k\ge 1$ is given and $\lambda>0$ is fixed and small, then there is a family of radial solutions exhibiting multiple blow-up as $\varepsilon\to 0$ in the form of a superposition of $k$ bubbles of different blow-up orders and shapes. Similar phenomena is found for the same problem involving the operator $\Delta_{N-\varepsilon}$ in $\mathbb R^N$, $N\ge 3$.
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