Quasilinear Evolution Integrodifferential Equations in Banach Spaces

Existence and uniqueness of local classical solutions of the quasilinear evolution integrodifferential equation in Banach spaces are studied. The results are demonstrated by employing the fixed point technique on C_0-semigroup of bounded linear operator. At last, we deal an example to interpret the theory.

___

  • [1] S. Abbas and D. Bahuguna, Existence of solutions to a quasilinear functional differential equations, Electronic Journal of Differential Equations, Vol. 2009(2009), no. 164, pp. 1–8.
  • [2] H. Aman, Quasilinear evolution equations and parabolic systems, Transactions of the American mathematical society, 293 (1986), no.1, 191-227.
  • [3] E. H. Anderson, M. J. Anderson and W.T. England, Nonhomogeneous quasilinear evolution equations, Journal of integral equations, 3(1981), no.2, 175-184.
  • [4] D. Bahuguna, Quasilinear integrodifferential equations in Banach spaces, Nonlinear Analysis 24 (1995), 175-183.
  • [5] D. Bahuguna, Regularity solutions to quasilinear integrodifferential equations in Banach spaces, Appl. Anal. 62 (1996), 1-9.
  • [6] K. Balachandran and D.G. Park, Existence of solutions of quasilinear integrodifferential evolution equations in Banach spaces, Bull. Korean Math. Soc., 46(2009), no.4, 691-700.
  • [7] R. S. Dubey, Existence of a Regular solution to quasilinear implicit integrodifferential equations in Banach space, Nonlinear Dynamics and Systems Theory,11(2) (2011) 137–146.
  • [8] R. Haloi, D. Bahuguna and D. N. Pandey, Electronic Journal of Differential Equations, Vol. 2012 (2012), No no. 13, pp. 1–10.
  • [9] S. Kato, Nonhomogeneous quasilinear evolution equations in Banach spaces, Nonlinear Analysis,9(1985), 1061-1071.
  • [10] T. Kato, Quasilinear equations of evolution with application to partial differential equations, Lecture Notes in Math. 448(1975), 25-70.
  • [11] A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1983.
  • [12] F. P. Samuel and K. Balachandran, Existence of solutions of quasilinear integrodifferential evolution equations with impulsive conditions, Thai Journal of Mathematics, 9(2011), no.1, 139-152.
  • [13] F. P. Samuel, T.R. Lisso and K.Z. Kaunda, Existence solutions for quasilinear evolution integrodifferential equations with infinite delay, International Journal of Engineering and Technical Research (IJETR), 2(4), April 2014.
  • [14] N. Sanekata, Abstract quasilinear equations of evolution in nonreflexive Banach spaces, Hiroshima Mathematical Journal, 19(1989), 109-139.
  • [15] K. Yosida, Functional Analysis, springer (1968).