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Volumn 348, Issue 1, 2008, Pages 137-149

Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients

Author keywords

Completely positive kernel; De Giorgi technique; Energy estimates; Fractional derivative; Integro differential equation; Quasilinear equation; Weak solution

Indexed keywords


EID: 50249156822     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.06.054     Document Type: Article
Times cited : (87)

References (17)
  • 1
    • 50249154447 scopus 로고    scopus 로고
    • E. Bazhlekova, Fractional evolution equations in Banach spaces, Dissertation, Technische Universiteit Eindhoven, 2001
    • E. Bazhlekova, Fractional evolution equations in Banach spaces, Dissertation, Technische Universiteit Eindhoven, 2001
  • 2
    • 43349101897 scopus 로고
    • On abstract Volterra equations in Banach spaces with completely positive kernels
    • Infinite-Dimensional Systems. Retzhof, 1983, Springer, Berlin
    • Clément Ph. On abstract Volterra equations in Banach spaces with completely positive kernels. Infinite-Dimensional Systems. Retzhof, 1983. Lecture Notes in Math. vol. 1076 (1984), Springer, Berlin 32-40
    • (1984) Lecture Notes in Math. , vol.1076 , pp. 32-40
    • Clément, Ph.1
  • 3
    • 0742286748 scopus 로고    scopus 로고
    • Quasilinear evolutionary equations and continuous interpolation spaces
    • Clément Ph., Londen S.-O., and Simonett G. Quasilinear evolutionary equations and continuous interpolation spaces. J. Differential Equations 196 (2004) 418-447
    • (2004) J. Differential Equations , vol.196 , pp. 418-447
    • Clément, Ph.1    Londen, S.-O.2    Simonett, G.3
  • 4
    • 0041427064 scopus 로고
    • Asymptotic behavior of solutions of nonlinear Volterra equations with completely positive kernels
    • Clément Ph., and Nohel J.A. Asymptotic behavior of solutions of nonlinear Volterra equations with completely positive kernels. SIAM J. Math. Anal. 12 (1981) 514-534
    • (1981) SIAM J. Math. Anal. , vol.12 , pp. 514-534
    • Clément, Ph.1    Nohel, J.A.2
  • 5
    • 0002969970 scopus 로고
    • Completely positive measures and Feller semigroups
    • Clément Ph., and Prüss J. Completely positive measures and Feller semigroups. Math. Ann. 287 (1990) 73-105
    • (1990) Math. Ann. , vol.287 , pp. 73-105
    • Clément, Ph.1    Prüss, J.2
  • 6
    • 51249167521 scopus 로고
    • Global existence for a semilinear parabolic Volterra equation
    • Clément Ph., and Prüss J. Global existence for a semilinear parabolic Volterra equation. Math. Z. 209 (1992) 17-26
    • (1992) Math. Z. , vol.209 , pp. 17-26
    • Clément, Ph.1    Prüss, J.2
  • 8
    • 1942542248 scopus 로고    scopus 로고
    • Cauchy problem for fractional diffusion equations
    • Eidelman S.E., and Kochubei A.N. Cauchy problem for fractional diffusion equations. J. Differential Equations 199 (2004) 211-255
    • (2004) J. Differential Equations , vol.199 , pp. 211-255
    • Eidelman, S.E.1    Kochubei, A.N.2
  • 9
    • 0011426570 scopus 로고
    • Volterra integro-differential equations with accretive nonlinearity
    • Gripenberg G. Volterra integro-differential equations with accretive nonlinearity. J. Differential Equations 60 (1985) 57-79
    • (1985) J. Differential Equations , vol.60 , pp. 57-79
    • Gripenberg, G.1
  • 10
    • 0003359314 scopus 로고
    • Volterra Integral and Functional Equations
    • Cambridge University Press, Cambridge
    • Gripenberg G., Londen S.-O., and Staffans O. Volterra Integral and Functional Equations. Encyclopedia Math. Appl. vol. 34 (1990), Cambridge University Press, Cambridge
    • (1990) Encyclopedia Math. Appl. , vol.34
    • Gripenberg, G.1    Londen, S.-O.2    Staffans, O.3
  • 11
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • Metzler R., and Klafter J. The random walk's guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339 (2000) 1-77
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 12
    • 0003223550 scopus 로고
    • Linear and Quasilinear Equations of Parabolic Type
    • Amer. Math. Soc., Providence, RI
    • Ladyzenskaja O.A., Solonnikov V.A., and Uralceva N.N. Linear and Quasilinear Equations of Parabolic Type. Transl. Math. Monogr. vol. 23 (1968), Amer. Math. Soc., Providence, RI
    • (1968) Transl. Math. Monogr. , vol.23
    • Ladyzenskaja, O.A.1    Solonnikov, V.A.2    Uralceva, N.N.3
  • 13
    • 0003334487 scopus 로고
    • Evolutionary Integral Equations and Applications
    • Birkhäuser, Basel
    • Prüss J. Evolutionary Integral Equations and Applications. Monogr. Math. vol. 87 (1993), Birkhäuser, Basel
    • (1993) Monogr. Math. , vol.87
    • Prüss, J.1
  • 14
    • 43349096659 scopus 로고    scopus 로고
    • Lyapunov functions and convergence to steady state for differential equations of fractional order
    • Vergara V., and Zacher R. Lyapunov functions and convergence to steady state for differential equations of fractional order. Math. Z. 259 (2008) 287-309
    • (2008) Math. Z. , vol.259 , pp. 287-309
    • Vergara, V.1    Zacher, R.2
  • 15
    • 17044365865 scopus 로고    scopus 로고
    • p for abstract parabolic Volterra equations
    • p for abstract parabolic Volterra equations. J. Evol. Equ. 5 (2005) 79-103
    • (2005) J. Evol. Equ. , vol.5 , pp. 79-103
    • Zacher, R.1
  • 16
    • 50249139776 scopus 로고    scopus 로고
    • Quasilinear parabolic integro-differential equations with nonlinear boundary conditions
    • Zacher R. Quasilinear parabolic integro-differential equations with nonlinear boundary conditions. Differential Integral Equations 19 (2006) 1129-1156
    • (2006) Differential Integral Equations , vol.19 , pp. 1129-1156
    • Zacher, R.1
  • 17
    • 50249085610 scopus 로고    scopus 로고
    • R. Zacher, Weak solutions of abstract evolutionary integro-differential equations in Hilbert spaces, Funkcial. Ekvac., in press
    • R. Zacher, Weak solutions of abstract evolutionary integro-differential equations in Hilbert spaces, Funkcial. Ekvac., in press


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