Cauchy Problem For A Class Of Pseudo-differential Equations On P-adic Field

In recent years,pseudo-differential equations on local field have attracted more and more attention due to their extensive applications in theoretical physics,fluid dynamics,and so on.The definition of the derivative of a function and the study of a class of pseudo-differential equations on Q_p have always been important issues in the field of local field research.In 1992,Su Weiyi used pseudo-differential operators to define the derivative and integral operators of functions on local compact Vilenkin groups G,which provided a theoretical basis for the study of pseudo-differential equations.Subsequently,many scholars have done a lot of research on the definite solution of a class of pseudo-differential equations on Q_p.On this basis,this paper mainly studies the Cauchy problem of a class of pseudo-differential equations on the n dimensional local field Q_p~n.By using Laplacian ?_p on the n dimensional local field Q_p~n,when the nonlinear term and initial value satisfy certain conditions,using the basic solution of the equation to obtain the expression of the solution of the pseudo-differential equation.