The global existence of small data solutions of certain viscoelastic evolution problems
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Date
2019-04-23
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University of Eloued جامعة الوادي
Abstract
We establish some new results concerning the initial value problem rst order
on the whole space Rn (n 1), the decay structure of which is of regularity-loss property.
By using Fourier transform and Laplace transform, we obtain the fundamental solutions and
thus the solution to the corresponding linear problem. Appealing to the point-wise estimate
in the Fourier space of solutions to the linear problem, we get estimates and properties of
solution operator, by exploiting which decay estimates of solutions to the linear problem
are obtained. Also by introducing a set of time-weighted Sobolev spaces and using the
contraction mapping theorem, we obtain the global in-time existence and the optimal decay
estimates of solutions to the semi-linear problem under smallness assumption on the initial
data.
Description
Working paper.3rd International Conference in Operator Theory, PDE and Applications. April 23-24- 2019. Faculty of Exact Science. Mathematics Department. University of ElOued
Keywords
global existence; small data solutions; certain viscoelastic; evolution problems
Citation
MELIK, Ammar. The global existence of small data solutions of certain viscoelastic evolution problems. 3rd International Conference in Operator Theory, PDE and Applications. April 23-24- 2019. Faculty of Exact Science. Mathematics Department. University of ElOued. [visited in ../../….]. available from [copy the link here]