GLOBAL EXISTENCE AND L~p ESTIMATES FOR SOLUTIONS OF DAMPED WAVE EQUATION WITH NONLINEAR CONVECTION IN MULTI-DIMENSIONAL SPACE

【摘要】 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.更多还原

【Abstract】 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.更多还原