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UID:8686@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250527T100000
DTEND;TZID=Europe/Paris:20250527T110000
DTSTAMP:20250523T122705Z
URL:https://www.i2m.univ-amu.fr/evenements/radial-blow-up-standing-solutio
 ns-for-the-semilinear-wave-equation/
SUMMARY:Maissâ Boughara (Universite Paris 13): Radial blow-up standing sol
 utions for the semilinear wave equation
DESCRIPTION:Maissâ Boughara: We consider the following semilinear wave equ
 ation with subconformal\npower nonlinearity in dimension $N$:\n$$\\partial
 ^2_t U=\\Delta U+|U|^{p-1}U\,$$\nwhere $p&gt\;1$ and if $N\\geq 2$ then $p
 \\leq 1+\\frac{4}{N-1}$. We are able\nconstruct a radial blow-up solution 
 which converges\, in similarity\nvariables\, to a soliton near $(r_0\, T (
 r_0))$ for a given $r_0&gt\;0$\,\nwhere $T(r_0)$ is the local blow-up time
 . For this purpose\, we use a\nmodulation technique allowing us to kill th
 e nonnegative modes of the\nlinearized operator of the equation around the
  soliton\, in similarity\nvariables. We will also use some energy estimate
 s from the one\ndimensional case\, with a new idea to control of some addi
 tional term we\nhave in our case. Combining all this with topological argu
 ment\, we are\nable to trap our error in some shrinking set for well chose
 n initial\ndata.
CATEGORIES:Séminaire,Analyse Appliquée
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