Global solution to the Cauchy problem of the nonlinear double dispersive wave equation with strong damping

Abstract

This paper concerns with the global classical solution to the Cauchy problem of the nonlinear double dispersive wave equation with strong damping uttuutt + � 2 u cut = d N X i=1 ∂ ∂xi σ i(uxi), where c and d are positive constants. By the contraction mapping principle and priori estimates, we prove that the Cauchy problem admits a unique global classical solution, and by the concavity method, we give the sufficient condi- tions on the blowup of the global solution of the Cauchy problem. Finally, as an application, an example is also given.