A Non-Linear Partial Differential Accretive Operator In A Closed, Bounded And Continuous Domain
Volume 1 - Issue 4, October 2017 Edition
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Author(s)
O. Echude, M. T. Y. Kadzai, A. A. Abubakar
Keywords
Accretive, operator, non-linear partial differential equation, Cauchy problem
Abstract
A non-linear parabolic partial differential equation is investigated in a closed, bounded and continuous domain by converting such an equation into an abstract Cauchy problem. Using some results established in Egwurube and Garba (2003), this operator is shown to be m-accretive thus establishing that this partial differential equation has a solution by the fundamental results of Browder (1967) on the theory of accretive operators.
References
[1] A. U. Bawa, M. O. Egwurube, &M. M. Ahmad, “A quasi-linear parabolic partial differential equation with accretive propertyâ€. Tanzania Journal of Natural and Applied Sciences. 3, pp. 433-438, 2012.
[2] F. E. Browder, “Non-linear mappings of non-expansive and accretive type in Banach spaceâ€. Bulletin of the American MathematicalSociety, 73, pp. 875 – 882, 1967.
[3] F. E. Browder, “Nonlinear monotone and accretive operators in Banach Spacesâ€. in Proceedings of the Symposium on Nonlinear Functional Analysis (August 1968) (American Mathematical Society). 61, pp. 388-393, 1968.
[4] F. E. Browder, “Non-linear operators and nonlinear equations of evolutions in Banach spaces, Non-linear functional analysisâ€, Proceedings of the Symposia on Pure Mathematics,American Mathematical Society, 18,(2), 1970.
[5] M. O. Egwurube, &E. J. D. Garba, “A Cauchy problem for a quasi-linear hyperbolic first-order partial differential equationâ€. Journal of Nigeria Association of Mathematical physics. 7, 29 – 32, 2003.
[6] Kartsatos A. G. “M-accretive-operatorsâ€, Encyclopedia of Mathematics:7 Feb 2011.URP: //www. encyclopediaofmath.org/index.php/M-accretive-operator
