|Title: ||Stable and unstable sets for damped nonlinear wave equations with variable exponent sources
||Author(s): ||Nhan L.C.
||Keywords: ||Nonlinear wave equations; Variable exponent sources
||Abstract: ||In this paper, we study a class of nonlinear wave equations with variable exponent sources. By introducing a family of potential wells, we first prove the global existence of solutions with initial data in the potential wells and the finite time blow-up for solutions starting in the unstable sets. The boundedness and asymptotic behavior of global solutions are also concerned. Finally, we obtain the finite time blow-up with high energy initial data.
||Issue Date: ||2021
||Publisher: ||American Institute of Physics Inc.
||Series/Report no.: ||Vol. 62
|Appears in Collections:||INTERNATIONAL PUBLICATIONS|