Systems of nonlinear wave equations with damping and supercritical boundary and interior sources Article

Guo, Y, Rammaha, MA. (2014). Systems of nonlinear wave equations with damping and supercritical boundary and interior sources . TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 366(5), 2265-2325. 10.1090/S0002-9947-2014-05772-3

cited authors

  • Guo, Y; Rammaha, MA

authors

abstract

  • We consider the local and global well-posedness of the coupled nonlinear wave equations in a bounded domain Ω ⊂ Rn with Robin and Dirichlét boundary conditions on u and v respectively. The nonlinearities f1(u, v) and f2(u, v) have supercritical exponents representing strong sources, while g1(ut) and g2(vt) act as damping. In addition, the boundary condition also contains a nonlinear source and a damping term. By employing nonlinear semigroups and the theory of monotone operators, we obtain several results on the existence of local and global weak solutions, and uniqueness of weak solutions. Moreover, we prove that such unique solutions depend continuously on the initial data. © 2014 American Mathematical Society.

publication date

  • February 26, 2014

published in

Digital Object Identifier (DOI)

start page

  • 2265

end page

  • 2325

volume

  • 366

issue

  • 5