Opuscula Mathematica
Opuscula Math. 34, no. 3 (), 569-590
http://dx.doi.org/10.7494/OpMath.2014.34.3.569
Opuscula Mathematica

Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity


Abstract. We prove the existence and uniqueness of a global decaying solution to the initial boundary value problem for the quasilinear wave equation with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a 'loan' method and use a difference inequality on the energy.
Keywords: global solutions, energy decay, quasilinear wave equation, Kelvin-Voigt dissipation, derivative nonlinearity.
Mathematics Subject Classification: 35B35, 35B40, 35L70.
Cite this article as:
Mitsuhiro Nakao, Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity, Opuscula Math. 34, no. 3 (2014), 569-590, http://dx.doi.org/10.7494/OpMath.2014.34.3.569
 
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.