| Abstract: |
| We discuss blow-up phenomena to solution of some classes of parabolic systems under Neumann boundary conditions and nonlinear hyperbolic coupled systems of fourth order under Dirichlet or Navier boundary conditions. The solutions may blow up in finite time $t^*$ and under appropriate assumptions on data, a safe interval of existence of the solution is derived with a lower bound of the lifespan. The proofs are based on some inequalities and coupled estimates techniques |
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