Local well posedness for strongly damped wave equations with critical nonlinearities

By Alexandre Nolasco de Carvalho, Jan W. Cholewa. Bulletin of the Australian Mathematical Society, 2002

95 citations recorded by the source corpus.

In this article the strongly damped wave equation is considered and a local well posedness result is obtained in the product space . The space of initial conditions is chosen according to the energy functional, whereas the approach used in this article is based on the theory of analytic semigroups as well as interpolation and extrapolation spaces. This functional analytic framework allows local existence results to be proved in the case of critically growing nonlinearities, which improves the existing results.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2556aec6a22baf36ccc944e2aeef8db6ae55c74d

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Citations in the corpus

Strongly damped wave problems: Bootstrapping and regularity of solutions (2008, methodology): “As shown in [2, 4], the knowledge of the scale of fractional power spaces and its embedding into known spaces are the main tool to obtain local well posedness of a semilinear sectorial problem (even in the critical growth case).”
Asymptotic regularity for some dissipative equations (2010, methodology): “For the case g(x) ∈ L2(Ω), the local existence of (4.1) was obtained by Carvalho and Cholewa [4] only under (4.2), and then the existence of a global attractor A in H was proved firstly by the same authors in [5] only under the assumptions (4.2)–(4.3) (actually, in [5], they considered a more genera”
Energy decay estimates for wave equations with a fractional damping (2012, methodology): “domain case (see Carvalho–Cholewa [2], Mugunolo [18], and the references therein).”
A model of viscoelasticity with time-dependent memory kernels (2016, background): “tray and Lions [10], this is the passage from viscoelasticity with long memory to viscoelasticity with short memory. In spite of a relatively vast literature concerning both (1.1) and (1.4) (see e.g. [1, 2, 4, 8, 16, 18, 19, 21, 22, 23, 24, 25, 26, 30] and references therein), we are not aware of an”