Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions
The Cauchy problem for a system of semilinear wave equations in two space dimensions and small initial data is studied. The nonlinear term is assumed to be the sum of a quadratic nonlinear term and a cubic nonlinear term. Inspired by known sufficient conditions for a global existence of solution -- the null conditions or the polynomial condition -- the author introduces a new structural condition for the cubic nonlinear term. It is then proved that if the quadratic null condition as well as the author's condition are satisfied, the stated Cauchy problem admits a unique global solution. Some examples of terms satisfying the author's condition are shown.
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