Title: Weak Solution and Weakly Uniformly Bounded Solution of Impulsive Heat Equations Containing “Maximum” Temperature
Author(s): Oyelami, Benjamin Oyediran
Pages: 131-150
Cite as:
Oyelami, Benjamin Oyediran, Weak Solution and Weakly Uniformly Bounded Solution of Impulsive Heat Equations Containing “Maximum” Temperature, Int. J. Anal. Appl., 3 (2) (2013), 131-150.

Abstract


In this paper, criteria for the existence of weak solutions and uniformly weak bounded solution of impulsive heat equation containing maximum temperature are investigated and results obtained. An example is given for heat flow system with impulsive temperature using maximum temperature simulator and criteria for the uniformly weak bounded of solutions of the system are obtained.

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References


  1. Erbe L.H., Freedman H.I., Liu X., Wu J.H., Comparison principles for impulsive parabolic equations with applications to models of single species growth, J. Austral. Math. Soc Ser. B.32 (1991) 382-400. Google Scholar

  2. Bainov D. D., Minchev E., Oscillation of the Solution of impulsive parabolic equations, J. Comput. Appli.Math. 69 (1996) 207-214. Google Scholar

  3. Bainov D.D., Kamont Z. and Minchev E., Monotone Iterative Methods for impulsive hyperbolic differential functional equations, J. Comput. Appl. Math. 70 (1996) 329-347. Google Scholar

  4. Bainov D. D., Minchev E., Estimates of solutions of impulsive parabolic systems, Applications to the population dynamics, Publ. Math. 40 (1996) 85-94. Google Scholar

  5. Bainov D. D., Minchev E. and Kiyokerizu Nakagawa. Asymptotic behavior of solution of impulsive Semilinear Parabolic equations. Nonlinear Analysis, Vol. 30, issues, Dec 1997, pp 2725 – 2734. Google Scholar

  6. Calderon A.P., Zygmund A. On the existence of certain singular integral Acta Mathematica 88(1), 1952, pp85-139. Google Scholar

  7. Calderon A.P., Zygmund A. On singular journal of Mathematics. The John Hopkins University press 78(2), 1956, pp 289-309. Google Scholar

  8. Cui B. T., Liu Y., Deng F., Some oscillation problems for impulsive hyperbolic differential systems with several delays Appl. Math. Comput. 146 (2003) 667 – 679. Google Scholar

  9. Gao W., Wang J., Estimates of solutions of impulsive parabolic equations under Neumann boundary conditions, J. Math. Anal. Appl. 283 (2003) 478-490. Google Scholar

  10. Lakshikantham V., Drici Z. Positive and boundedness of solutions of impulsive-diffusion equations.J.Computation and Applied Math (1998), 175-184. Google Scholar

  11. Lax Peter D. Milgram Arthur N (1954) parabolic equation. Contribution to the theory of partial differential equations. Anals of maths studia, no. 33, Princeton University press pp 167 – 190. Google Scholar

  12. Luo J. Oscillation of hyperbolic PDE with Impulses. Applic Math. Computation 2002. Google Scholar

  13. Oyelami B O and Ale Impulsive differential equations and applications to some models. Lambert Academic Publisher Germany, Mar 2012, ISBN 978-3-8484-4740-4. Google Scholar

  14. Oyelami B O and Ale, On existence of solution, oscillation and non-oscillation properties of delay equations containing ‘Maximum' Acta Applicandae Mathematicae, 2010, 109,683-701. Google Scholar

  15. Oyelami B O, Studies on impulsive Systems: Theory and Modeling Lambert Academic Publisher Germany, Dec. 2012, ISBN 978-3-659-20724-2. Google Scholar

  16. Remaswamy J. The Lax-Milgram theorem for Banach Space.Proc. Jpm Acad. Ser A, 56, 462 – 464 (1980) Google Scholar

  17. Fu X., Liu X., Sivaloganathan S., Oscillation criteria for impulsive parabolic systems, Appl. Anal. 79 (2001) 239-255. Google Scholar

  18. Fu X., Liu X., Sivaloganathan S., Oscillation criteria for impulsive parabolic differential equations with delay, J. Math. Anal. Appl. 268 (2002) 647 – 664. Google Scholar