%0 Journal Article
%T Solvability of Nonlinear Goursat Type Problem for Hyperbolic Equation with Integral Condition
%J Khayyam Journal of Mathematics
%I Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
%Z 2423-4788
%A Oussaeif, Taki Eddine
%A Bouziani, Abdelfatah
%D 2018
%\ 07/01/2018
%V 4
%N 2
%P 198-213
%! Solvability of Nonlinear Goursat Type Problem for Hyperbolic Equation with Integral Condition
%K Energy inequality
%K Goursat equation
%K nonlinear hyperbolic problems
%K integral condition
%K a priori estimate
%R 10.22034/kjm.2018.65161
%X This paper is concerned with the existence and uniqueness of a strong solution for linear problem by using a functional analysis method, which is based on an energy inequality and the density of the range of the operator generated by the problem. Applying an iterative process based on results obtained from the linear problem, we prove the existence anduniqueness of the weak generalized solution of nonlinear hyperbolic Goursat problem with integral condition.
%U http://www.kjm-math.org/article_65161_8fed2a0e71a8af7d76b734e82401f3b2.pdf