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

MSC:
35K60Nonlinear initial 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
[2] Byszewski, L.: Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. J. math. Anal. appl. 162, 494-505 (1991) · Zbl 0748.34040
[3] Henry, D.: Geometric theory of semilinear parabolic equations, lecture notes in mathematics 840. (1981)
[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. · Zbl 1083.34045
[7] Lin, Y.; Liu, James: Semilinear integrodifferential equations with nonlocal Cauchy problem. Nonlinear anal. Theory methods appl. 26, 1023-1033 (1996) · Zbl 0916.45014
[8] Lunardi, A.: Analytic semigroups and optimal regularity in parabolic problems. (1995) · Zbl 0816.35001
[9] Tanabe, H.: Functional analytic methods for partial differential equations. (1997) · Zbl 0867.35003