A Cauchy Problem For A Class Of Nonlinear Hyperbolic First Order Partial Differential Equation In A Banach Space
Volume 4 - Issue 2, February 2020 Edition
[Download Full Paper]
O. Echude, B. Balarabe, H. Mohammed
Accretive, Cauchy Problem, Non-linear PDE, Hyperbolic
The ultimate work done in this research is the vast and active field of nonlinear hyperbolic first order partial differential equations. A class of nonlinear hyperbolic first order partial differential equation in a Banach space was investigated by converting it to Cauchy-like equation, than show that the operator A is accretive, M-accretive and thus admit a solution.
 D. K. Gvazava (originator), Quasi-linear hyperbolic equations and systems. Encyclopedia of Mathematics. URP:http://www.encyclopediaofmath.org/index.php?title=Quasilinear_hyperbolic_equations_and_systems&oldid=16213
 E. Levi, "Sur problema di Cauchy per le equazioni a caratteristiche reali e distinti" Rend. R. Acad. Lincei (5) , 17 (1908) pp. 331–339
 M. O. Egwurube, & E. J. D. Garba, “A Cauchy problem for a quasi-linear hyperbolic first-order partial differential equation”. Journal of Nigeria Association of Mathematical Physics, 7, 29 – 32. 2003.
 A. U. Bawa, M. O. Egwurube, & M. M. Ahmad, “A quasi-linear parabolic partial differential equation with accretive property”. Tanzania Journal of Natural and Applied Sciences. 3, 433-438, 2012.
 O. Echude, M. T. Y. Kadzai and A. A. Abubakar, “A non-linear partial differential accretive operator in a closed, bounded and continuous domain”. International Journal of Advanced Research and Publications (IJARP); Volume 1, (2017), 84-87
 F. E. Browder, “Non-linear mappings of non-expansive and accretive type in Banach space”. Bulletin of the American Mathematical Society, 73, 875 – 882, 1967.
 F. E. Browder, “Nonlinear monotone and accretive operators in Banach Spaces”. in Proceedings of the Symposium on Nonlinear Functional Analysis (August 1968) (American Mathematical Society). 61, 388-39, 1968.