NONLINEAR DISPERSIVE WAVE EQUATIONS IN TWO SPACE DIMENSIONS

作者：Hayashi Nakao^*; Kobayashi Seishirou; Naumkin Pavel I

来源：Communications on Pure and Applied Analysis, 2015, 14(4): 1377-1393.

DOI：10.3934/cpaa.2015.14.1377

• Dispersive nonlinear wave
• asymptotic behavior
• system of equations
• global in time of solutions
• vector field method

We study the global existence and time decay of solutions to non-linear dispersive wave equations partial derivative(2)(t)u + 1/rho(2) (-Delta)(rho) u = F (partial derivative(t)u) in two space dimensions, where F (partial derivative(t)u) = lambda vertical bar partial derivative(t)u vertical bar(p-1) partial derivative(t)u or lambda vertical bar partial derivative(t)u vertical bar(p), lambda is an element of C; with p > 2 for 0 < rho < 1, p > 3 for rho = 1, and p > 1 + rho for 1 < rho < 2. If rho = 1; then the equation converts into the well-known nonlinear wave equation.

• 出版日期2015-7