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Existence of classical solutions to nonautonomous nonlocal parabolic problems. (English) Zbl 1159.35383


MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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References:

[1] Aizicovici, S.; McKibben, M., Existence results for a class of abstract nonlocal Cauchy problems, Nonlinear Anal., Ser. ATheory Methods, 39, 649-668 (2000) · Zbl 0954.34055
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[3] Henry, D., Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics 840 (1981), Springer: Springer Berlin, New York
[4] Jackson, D., Existence and uniqueness of solutions to semilinear nonlocal parabolic equations, J. Math. Anal. Appl., 172, 256-265 (1993) · Zbl 0814.35060
[5] Liang, J.; van Casteren, J.; Xiao, T. J., Nonlocal Cauchy problems for semilinear evolution equations, Nonlinear Anal., Ser. ATheory Methods, 50, 173-189 (2002) · Zbl 1009.34052
[6] J. Liang, James Liu, T.J. Xiao, Nonlocal Cauchy problems governed by compact operator families, Nonlinear Anal., Ser. A: Theory Methods 57 (2004) 183-189.; J. Liang, James Liu, T.J. Xiao, Nonlocal Cauchy problems governed by compact operator families, Nonlinear Anal., Ser. A: Theory Methods 57 (2004) 183-189. · Zbl 1083.34045
[7] Lin, Y.; James Liu, Semilinear integrodifferential equations with nonlocal Cauchy problem, Nonlinear Anal. Theory Methods Appl., 26, 1023-1033 (1996) · Zbl 0916.45014
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[9] Tanabe, H., Functional Analytic Methods for Partial Differential Equations (1997), Marcel Dekker: Marcel Dekker New York · Zbl 0867.35003
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