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Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains

M. Bochniak, Anna-Margarete Sändig (1999)

Mathematica Bohemica

We consider a class of semilinear elliptic problems in two- and three-dimensional domains with conical points. We introduce Sobolev spaces with detached asymptotics generated by the asymptotical behaviour of solutions of corresponding linearized problems near conical boundary points. We show that the corresponding nonlinear operator acting between these spaces is Frechet differentiable. Applying the local invertibility theorem we prove that the solution of the semilinear problem has the same asymptotic...

Long-time asymptotics of solutions to some nonlinear wave equations

Grzegorz Karch (2000)

Banach Center Publications

In this paper, we survey some recent results on the asymptotic behavior, as time tends to infinity, of solutions to the Cauchy problems for the generalized Korteweg-de Vries-Burgers equation and the generalized Benjamin-Bona-Mahony-Burgers equation. The main results give higher-order terms of the asymptotic expansion of solutions.

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