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Evolution equation associated with the power of the Gross Laplacian

GFM seminar
CIUL, B2-01
2006-12-19 14:00 .. 15:00
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by Habib Ouerdiane (Univ. Tunis El-Manar, Tunisia)

We study an evolution equation associated with the power of the Gross Laplacian ΔpG and a potential function V on an infinite dimensional space. The initial condition is a generalized function. The main technique we use is the representation of the Gross Laplacian as a convolution operator. This representation enables us to apply the convolution calculus on a suitable distribution space to obtain the explicit solution of the perturbed evolution equation. Our results generalize those previously obtained by Hochberg in the one-dimensional case with V=0, as well as by Barhoumi-Kuo-Ouerdiante for the case p=1.