×

zbMATH — the first resource for mathematics

Semilinear integrodifferential equations with nonlocal initial conditions. (English) Zbl 1068.45014
The paper is concerned with developing existence and uniqueness theorems for the Cauchy problem for semilinear integro-differential equations of convolution type. The sequence of theorems presented extends the existing results and can be applied, as is shown in the final section of the paper, to problems that arise in heat conduction in materials with memory.

MSC:
45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] 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
[2] Boucherif, A, First-order differential inclusions with nonlocal initial conditions, Appl. math. lett., 15, 4, 409-414, (2002) · Zbl 1025.34009
[3] Byszewski, L; Byszewski, L, Application of properties of the right-hand sides of evolution equations to an investigation of nonlocal evolution problems, Nonlinear anal. TMA, Nonlinear anal. TMA, 34, 65-72, (1998) · Zbl 0933.34064
[4] Jackson, D, Existence and uniqueness of solutions of a 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. A: theory methods, 50, 173-189, (2002) · Zbl 1009.34052
[6] Lin, Y; Liu, J.H, Semilinear integrodifferential equations with nonlocal Cauchy problem, Nonlinear anal. TMA, 26, 1023-1033, (1996) · Zbl 0916.45014
[7] Ntouyas, S.K; Tsamatos, P.Ch, Global existence for semilinear evolution equations with nonlocal conditions, J. math. anal. appl., 210, 679-687, (1997) · Zbl 0884.34069
[8] Pazy, A, Semigroups of linear operators and applications to partial differential equations, (1983), Springer-Verlag New York · Zbl 0516.47023
[9] Grimmer, R, Resolvent operators for integral equations in a Banach space, Trans. amer. math. soc., 273, 333-349, (1982) · Zbl 0493.45015
[10] Fattorini, H.O, The Cauchy problem, (1983), Addison-Wesley Reading, MA · Zbl 0493.34005
[11] Engel, K.-J; Nagel, R, ()
[12] Goldstein, J.A, Semigroups of linear operators and applications, (1985), Oxford Univ. Press New York · Zbl 0592.47034
[13] van Casteren, J, Generators of strongly continuous semigroups, (1985), Pitman London · Zbl 0576.47023
[14] Xiao, T.J; Liang, J, ()
[15] Chen, G, Control and stabilization for the wave equation in a bounded domain, SIAM J. control, 17, 66-81, (1979) · Zbl 0402.93016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.