Existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping

@article{Sun2007ExistenceAN,
  title={Existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping},
  author={Fuqin Sun and M. Wang},
  journal={Nonlinear Analysis-theory Methods & Applications},
  year={2007},
  volume={66},
  pages={2889-2910}
}
  • Fuqin Sun, M. Wang
  • Published 2007
  • Mathematics
  • Nonlinear Analysis-theory Methods & Applications
  • Abstract This paper concerns with the Cauchy problem for the damped nonlinear hyperbolic system { u t t − △ u + u t = | v | p , ( t , x ) ∈ R + 1 × R N , v t t − △ v + v t = | u | q , ( t , x ) ∈ R + 1 × R N , u ( 0 , x ) = u 0 ( x ) , u t ( 0 , x ) = u 1 ( x ) , x ∈ R N , v ( 0 , x ) = v 0 ( x ) , v t ( 0 , x ) = v 1 ( x ) , x ∈ R N , where p , q ≥ 1 and satisfy p q > 1 . We shall prove that if max { 1 + p p q − 1 , 1 + q p q − 1 } N 2 for N = 1 or 3, then the solution with small initial data… CONTINUE READING
    41 Citations
    Large time behavior of solutions for a system of nonlinear damped wave equations
    • 20
    • Highly Influenced
    • PDF
    The critical exponent for the dissipative plate equation with power nonlinearity
    • M. D'Abbicco
    • Mathematics, Computer Science
    • Comput. Math. Appl.
    • 2017
    • 2