Stability Of The Transport Equation

In this paper,we consider the first order linear partial differential equations of diagonal type with two independent variables,represented by the following vector equation:U_t(x,t)+AU_x(x,t)=BU(x,t),among them,(?) and u_t(x,t)+au_x(x,t)= bu(x,t) is transport equation,the most basic equation.The purpose of this thesis is to study the influence of the coefficients in front of the unknown function U(x,t)on the stability of the solution of the transmission system under different conditions.The main work of this paper is in Chapter IV and Chapter V.In Chapter IV,first construct Lyapunov function,apply the stability theorem to study the influence of the coefficients in front of the unknown function U(x,t)on the stability of the solution of the transmission system.In Chapter V,change the right boundary to the move boundary,thus,the feasible region changes from columnar region to non-columnar region,we study that the influence of the coefficients on the stability of the solution of the transport equation will no change at this time.