id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-418	Kilicman, Adem; Eltayeb, Hassan	On the Partial Differential Equations with Non-Constant Coefficients and Convolution Method	2009	6	.pdf	application/pdf	2009	108	77	Now consider the equations (5) and (11) have solutions F(x , t) and K(x , t) respectively, then we can easily check whether F(x , t) ∗ ∗K(x , t) is a solution for a similar type of wave equation. Now by taking double Laplace transform for the equation (11) and single Laplace transform for initial conditions, the solution of equation (11) given by u(x , t) = L−1 s L−1 p      sH1(p) � s2 − p2 � − pG1(s) � s2 − p2 � + pH1(p)−H1(0) � s2 − p2 � − sG1(s)− G1(0) � s2 − p2 � + F(p, s) � s2 − p2 � Ψ(p, s)      (12) provided the inverse double Laplace transform exist.	cache/ejpam-418.pdf	txt/ejpam-418.txt