Geodesic
On blow-up of solutions of the Kuramoto-Sivashinsky equation
Sbornik. Mathematics, Tome 199 (2008) no. 9, pp. 1355-1365 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of the absence of global solutions of initial-boundary value problems for the Kuramoto-Sivashinsky equation is considered. Sufficient conditions for the absence of global solutions of the problems under consideration are obtained both for bounded and unbounded domains. These conditions imply a priori the blow-up of the solution of the corresponding initial-boundary value problem. The proof uses a generalization of the method of non-linear capacity based on the choice of asymptotically optimal test functions. Bibliography: 20 titles. 
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S. I. Pokhozhaev. On blow-up of solutions of the Kuramoto-Sivashinsky equation. Sbornik. Mathematics, Tome 199 (2008) no. 9, pp. 1355-1365. http://geodesic.mathdoc.fr/item/SM_2008_199_9_a1/

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