Guangqing(毕光庆) (Yan’an Second School,Yan’an,716000) Abstract For linear partial differential equation P( x, t)u=f(x,t), where x∈R n,t∈R 1. With P( x, t) is (t+P( x)) m,∏mi=1(t-a iP( ...Guangqing(毕光庆) (Yan’an Second School,Yan’an,716000) Abstract For linear partial differential equation P( x, t)u=f(x,t), where x∈R n,t∈R 1. With P( x, t) is (t+P( x)) m,∏mi=1(t-a iP( x)) or ∏mi=1( 2t 2-a 2 iP( x)),the author gives the analytic solution of the initial value problem using the operators e tP( x) and sh(tP( x) 1/2 )P( x) 1/2 . By representing the operators with integrals,explicit solutions are obtained with an integral form of a given function.展开更多
We summarize several relevant principles for the application of abstract operators in partial differential equations, and combine abstract operators with the Laplace transform. Thus we have developed the theory of par...We summarize several relevant principles for the application of abstract operators in partial differential equations, and combine abstract operators with the Laplace transform. Thus we have developed the theory of partial differential equations of abstract operators and obtained the explicit solutions of initial value problems for a class of higher-order linear partial differential equations.展开更多
文摘Guangqing(毕光庆) (Yan’an Second School,Yan’an,716000) Abstract For linear partial differential equation P( x, t)u=f(x,t), where x∈R n,t∈R 1. With P( x, t) is (t+P( x)) m,∏mi=1(t-a iP( x)) or ∏mi=1( 2t 2-a 2 iP( x)),the author gives the analytic solution of the initial value problem using the operators e tP( x) and sh(tP( x) 1/2 )P( x) 1/2 . By representing the operators with integrals,explicit solutions are obtained with an integral form of a given function.
文摘We summarize several relevant principles for the application of abstract operators in partial differential equations, and combine abstract operators with the Laplace transform. Thus we have developed the theory of partial differential equations of abstract operators and obtained the explicit solutions of initial value problems for a class of higher-order linear partial differential equations.
