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http://dx.doi.org/10.4134/BKMS.2009.46.4.691

EXISTENCE OF SOLUTIONS OF QUASILINEAR INTEGRODIFFERENTIAL EVOLUTION EQUATIONS IN BANACH SPACES  

Balachandran, Krishnan (DEPARTMENT OF MATHEMATICS BHARATHIAR UNIVERSITY)
Park, Dong-Gun (DEPARTMENT OF MATHEMATIC DONG-A UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.46, no.4, 2009 , pp. 691-700 More about this Journal
Abstract
We prove the local existence of classical solutions of quasi-linear integrodifferential equations in Banach spaces. The results are obtained by using fractional powers of operators and the Schauder fixed-point theorem. An example is provided to illustrate the theory.
Keywords
existence of solution; quasilinear integrodifferential equation; analytic semigroup; fixed point theorem;
Citations & Related Records

Times Cited By Web Of Science : 3  (Related Records In Web of Science)
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연도 인용수 순위
1 K. Balachandran and K. Uchiyama, Existence of solutions of quasilinear integrodifferential equations with nonlocal condition, Tokyo J. Math. 23 (2000), no. 1, 203–210
2 F. Colombo, Quasilinear parabolic equations in Ck spaces, Dynam. Systems Appl. 6 (1997), no. 2, 271–296
3 N. Sanekata, Abstract quasi-linear equations of evolution in nonreflexive Banach spaces, Hiroshima Math. J. 19 (1989), no. 1, 109–139
4 D. Bahuguna, Regular solutions to quasilinear integrodifferential equations in Banach spaces, Appl. Anal. 62 (1996), no. 1-2, 1–9   DOI   ScienceOn
5 H. Amann, Quasilinear evolution equations and parabolic systems, Trans. Amer. Math. Soc. 293 (1986), no. 1, 191–227
6 E. H. Anderson, M. J. Anderson, and W. T. England, Nonhomogeneous quasilinear evolution equations, J. Integral Equations 3 (1981), no. 2, 175–184
7 D. Bahuguna, Quasilinear integrodifferential equations in Banach spaces, Nonlinear Anal. 24 (1995), no. 2, 175–183   DOI   ScienceOn
8 M. G. Crandall and P. E. Souganidis, Convergence of difference approximations of quasilinear evolution equations, Nonlinear Anal. 10 (1986), no. 5, 425–445   DOI   ScienceOn
9 A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, Inc., New York, 1969
10 R. Ikehata and N. Okazawa, A class of second order quasilinear evolution equations, J. Differential Equations 114 (1994), no. 1, 106–131   DOI   ScienceOn
11 A. Lunardi, Global solutions of abstract quasilinear parabolic equations, J. Differential Equations 58 (1985), no. 2, 228–242   DOI
12 S. Kato, Nonhomogeneous quasilinear evolution equations in Banach spaces, Nonlinear Anal. 9 (1985), no. 10, 1061–1071   DOI   ScienceOn
13 T. Kato, Quasi-linear equations of evolution, with applications to partial differential equations, Spectral theory and differential equations (Proc. Sympos., Dundee, 1974; dedicated to Konrad Jorgens), pp. 25–70. Lecture Notes in Math., Vol. 448, Springer, Berlin, 1975   DOI
14 K. Kobayasi and N. Sanekata, A method of iterations for quasi-linear evolution equations in nonreflexive Banach spaces, Hiroshima Math. J. 19 (1989), no. 3, 521–540
15 M. G. Murphy, Quasilinear evolution equations in Banach spaces, Trans. Amer. Math. Soc. 259 (1980), no. 2, 547–557
16 H. Oka and N. Tanaka, Abstract quasilinear integrodifferential equations of hyperbolic type, Nonlinear Anal. 29 (1997), no. 8, 903–925   DOI   ScienceOn
17 A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983
18 P. E. Sobolevskii, Equations of parabolic type in Banach space, Amer. Math. Soc. Transl. 49 (1965), 1-62
19 N. Tanaka, Quasilinear evolution equations with non-densely defined operators, Differential Integral Equations 9 (1996), no. 5, 1067–1106
20 K. Furuya, Analyticity of solutions of quasilinear evolution equations. II, Osaka J. Math. 20 (1983), no. 1, 217–236
21 N. Sanekata, Convergence of approximate solutions to quasilinear evolution equations in Banach spaces, Proc. Japan Acad. Ser. A Math. Sci. 55 (1979), no. 7, 245–249   DOI
22 N. Sanekata, Abstract quasi-linear equations of evolution with application to first order quasi-linear hyperbolic systems in two independent variables, Adv. Math. Sci. Appl. 3 (1993/94), Special Issue, 119–159
23 K. Balachandran and K. Uchiyama, Existence of local solutions of quasilinear integrodifferential equations in Banach spaces, Appl. Anal. 76 (2000), no. 1-2, 1–8   DOI   ScienceOn
24 T. Kato, Abstract evolution equations, linear and quasilinear, revisited, Functional analysis and related topics, 1991 (Kyoto), 103–125, Lecture Notes in Math., 1540, Springer, Berlin, 1993   DOI
25 A. G. Kartsatos, Perturbations of M-accretive operators and quasi-linear evolution equations, J. Math. Soc. Japan 30 (1978), no. 1, 75–84   DOI
26 H. Oka, Abstract quasilinear Volterra integrodifferential equations, Nonlinear Anal. 28 (1997), no. 6, 1019–1045   DOI   ScienceOn