Tao, Qiang; Gao, Hang; Zhang, Bo Approximate controllability of a parabolic equation with memory. (English) Zbl 1238.93018 Nonlinear Anal., Hybrid Syst. 6, No. 2, 839-845 (2012). Summary: We study the approximate controllability of a parabolic equation with memory \(y_t + y_{xx} + \int^t_0 y(x,s)ds = 0\) by boundary control. The proof relies on the explicit solution of the corresponding homogeneous initial boundary value problem and a duality method. Cited in 7 Documents MSC: 93B05 Controllability 93C20 Control/observation systems governed by partial differential equations 35R09 Integro-partial differential equations Keywords:approximate controllability; parabolic integrodifferential equation; memory PDFBibTeX XMLCite \textit{Q. Tao} et al., Nonlinear Anal., Hybrid Syst. 6, No. 2, 839--845 (2012; Zbl 1238.93018) Full Text: DOI References: [1] Volterra, V., Theory of Functionals (1930), Blackie and Son Ltd · JFM 56.1010.01 [2] Yamada, Y., On a certain class of semilinear Volterra diffusion equations, J. Math. Anal. Appl., 88, 433-457 (1982) · Zbl 0515.45012 [3] Yamada, Y., Asymptotic stability for some systems of semilinear Volterra diffusion equations, J. Differ. Equ., 52, 295-326 (1984) · Zbl 0543.35053 [4] Zhang, N. Y., On fully discrete Galerkin approximations for partial integrodifferential equations of parabolic type, Math. Comp., 60, 133-166 (1993) · Zbl 0795.65098 [5] Blanchard, D.; Ghidouche, H., A nonlinear system for irreversible phase changes, European J. Appl. Math., 1, 91-100 (1990) · Zbl 0713.35045 [6] Barbu, V.; Iannelli, M., Controllability of the heat equation with memory, Differ. Integral Equ., 13, 1393-1412 (2000) · Zbl 0990.93008 [7] Fu, X.; Yong, J.; Zhang, X., Controllability and observability of a heat equation with hyperbolic memory kernel, J. Differ. Equ., 247, 2395-2439 (2009) · Zbl 1187.35265 [8] Sakthivel, K.; Balachandran, K.; Nagaraj, B. R., On a class of non-linear parabolic control systems with memory effects, Internat. J. Control, 81, 764-777 (2008) · Zbl 1152.93312 [9] Lavanya, R.; Balachandran, K., Null controllability of nonlinear heat equations with memory effects, Nonlinear Anal. Hybrid Syst., 3, 163-175 (2009) · Zbl 1166.93004 [10] Prüss, J., Evolutionary Integral Equations and Applications (1993), Birkhäuser-Verlag: Birkhäuser-Verlag Basel · Zbl 0793.45014 [11] Rosier, L.; Rouchon, P., On the controllability of a wave equation with structural damping, Int. J. Tomogr. Stat., 5, 79-84 (2007) 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.