四阶p-广义Benney-Luke方程的初值问题

The Cauchy Problem for the Forth Order p-Generalized Benney-Luke Equation

研究了四阶p-广义Benney-Luke方程的初值问题在自然能量空间H˙^(1)(R^(n))∩H˙^(2)(R^(n))×H^(1)(R^(n))中解的整体存在性和唯一性.首先利用压缩映像原理证明解在能量空间中的局部存在性和唯一性.其次当非线性项为源项时给出解整体存在的充分条件.

We consider the global existence and uniqueness of the Cauchy problem for the forth order p-generalized Benney Luke equatoion in the natural energy space H˙^(1)(R^(n))∩H˙^(2)(R^(n))×H^(1)(R^(n)).First of all,the local existence and uniqueness of solutions are investigated in the energy space by means of the contraction mapping principle.Secondly,in the case of source nonlinearity,we provide the sufficient conditions of the existence of global solutions.