In this article, the author studies the Cauchy problem of the damped wave equation with a nonlinear convection term in multi-dimensions. The author shows that a classical solution to the Cauchy problem exists globally...In this article, the author studies the Cauchy problem of the damped wave equation with a nonlinear convection term in multi-dimensions. The author shows that a classical solution to the Cauchy problem exists globally in time under smallness condition on the initial perturbation. Furthermore, the author obtains the L^p （2 ≤ p ≤ ∞） decay estimates of the solution.展开更多
基金supported by Shanghai Municipal Natural Science Foundation 09ZR1413500National Natural Science Foundation of China 11071162
文摘In this article, the author studies the Cauchy problem of the damped wave equation with a nonlinear convection term in multi-dimensions. The author shows that a classical solution to the Cauchy problem exists globally in time under smallness condition on the initial perturbation. Furthermore, the author obtains the L^p （2 ≤ p ≤ ∞） decay estimates of the solution.
