Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping

abstract

• 2014 Elsevier Inc. Presented here is a study of a viscoelastic wave equation with supercritical source and damping terms. We employ the theory of monotone operators and nonlinear semigroups, combined with energy methods to establish the existence of a unique local weak solution. In addition, it is shown that the solution depends continuously on the initial data and is global provided the damping dominates the source in an appropriate sense.

authors

• Titi, Edriss

published proceedings

• JOURNAL OF DIFFERENTIAL EQUATIONS

altmetric score

• 0.25

author list (cited authors)

• Guo, Y., Rammaha, M. A., Sakuntasathien, S., Titi, E. S., & Toundykov, D.

citation count

• 22

complete list of authors

• Guo, Yanqiu||Rammaha, Mohammad A||Sakuntasathien, Sawanya||Titi, Edriss S||Toundykov, Daniel

publication date

• November 2014

publisher

• Elsevier  Publisher

published in

• Journal of Differential Equations  Journal

keywords

• Damping And Sources
• Integro-differential
• Memory
• Monotone Operators
• Nonlinear Semigroup
• Viscoelastic

Digital Object Identifier (DOI)

• 10.1016/j.jde.2014.07.009

start page

• 3778

end page

• 3812

volume

• 257

issue

• 10

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.jde.2014.07.009