Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 23
Number of page(s) 16
DOI https://doi.org/10.1051/cocv/2023013
Published online 30 March 2023
  1. P. Cannarsa, H. Frankowska and E.M. Marchini, Optimal control for evolution equations with memory. J. Evol. Equ. 13 (2013) 197–227. [CrossRef] [MathSciNet] [Google Scholar]
  2. P. Cannarsa and D. Sforza, Global solutions of abstract semilinear parabolic equations with memory terms. Nonlinear Diff. Equ. Appl. 10 (2003) 399–430. [Google Scholar]
  3. E. Casas, Second order analysis for bang-bang control problems of PDEs. SIAM J. Control Optim. 50 (2022) 2355–2372. [Google Scholar]
  4. E. Casas and K. Kunisch, Optimal control of semilinear parabolic equations with non-smooth pointwise-integral control constraints in time-space. Appl. Math. Optim. 85 (2022). [CrossRef] [Google Scholar]
  5. E. Casas and K. Kunisch, Infinite horizon optimal control for a general class of semilinear parabolic equations (2022) Submitted. [Google Scholar]
  6. E. Casas and M. Mateos, Critical cones for sufficient second order conditions in PDE constrained optimization. SIAM J. Optim. 30 (2020) 585–603. [Google Scholar]
  7. E. Casas, C. Ryll and F. Tröltzsch, Optimal control of a class of reaction-diffusion systems. Comput. Optim. Appl. 70 (2018) 677–707. [CrossRef] [MathSciNet] [Google Scholar]
  8. E. Casas and F. Tröltzsch, Second order analysis for optimal control problems: improving results expected from abstract theory. SIAM J. Optim. 22 (2012) 261–279. [CrossRef] [MathSciNet] [Google Scholar]
  9. E. Casas and F. Trooltzsch, Second order optimality conditions for weak and strong local solutions of parabolic optimal control problems. Vietnam J. Math. 44 (2016) 181–202. [Google Scholar]
  10. A. Constantin and S. Peszat, Global existence of soutions of semilinear parabolic evolution equations. Diff. Int. Equ. 13 (2000) 99–114. [Google Scholar]
  11. K. Disser, A.F.M. ter Elst and J. Rehberg, Hölder estimates for parabolic operators on domains with rough boundary. Ann. Sc. Norm. Super. Pisa Cl. Sci. 17 (2017) 65–79. [Google Scholar]
  12. K. Ezzinbi and P. Ndambomve, Solvability of some partial functional integrodifferential equations with finite delay and optimal controls in Banach spaces. SpringerPlus 5 (2016) 1264. [Google Scholar]
  13. Z.B. Fang and L Qiu, Global existence and uniform energy decay rates for the semilinear parabolic equation with a memory term and mixed boundary condition. Abst. Appl. Anal. (2013) 532935 https://doi-org.unican.idm.oclc.org/10.1155/2013/532935. [Google Scholar]
  14. P. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms. Springer-Verlag, Berlin, Heidelberg, New York, Tokio (1986). [CrossRef] [Google Scholar]
  15. M.E. Gurtin and A.C. Pipkin, A general theory of heat conduction with finite wave speeds. Arch. Ratl. Mech. Anal. 31 (1968) 113–126. [CrossRef] [Google Scholar]
  16. D. Henry, Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math., Vol. 840, Springer-Verlag (1981). [Google Scholar]
  17. B. Hu, Blow-up Theories for Semilinear Parabolic Equation. Springer (2011). [CrossRef] [Google Scholar]
  18. S. Larsson, Semilinear parabolic partial differential equations: theory, approximation, and application. New Trends in the Mathematical and Computer Sciences, 153–194, Publ. ICMCS, 3, Int. Cent. Math. Comp. Sci. (ICMCS), Lagos (2006). [Google Scholar]
  19. O.A. Ladyzhenskaya, V.A. Solonnikov and N.N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type. American Mathematical Society, Providence (1988). [Google Scholar]
  20. J.W. Nunziato, On heat conduction in materials with memory. Quart. Appl. Math. (1971) 187–204. [Google Scholar]
  21. W. Rudin, Real and Complex Analysis. McGraw-Hill Book Co., London (1970). [Google Scholar]
  22. J. Shi, C. Wang and H. Wang, Diffusive spatial movement with memory and maturation delays. Nonlinearuy 32 (2019) 3188–3208. [Google Scholar]
  23. R.E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, volume 49 of Math. Surv. and Monogr. American Mathematical Society, Providence, RI (1997). [Google Scholar]
  24. D. Sofiane, B. Abdelfatah and O. Taki-Eddine, Study of solution for a parabolic intergodifferential equation with the second kind integral condition. Int. J. Anal. Appl. 16 (2018) 569–593. [Google Scholar]
  25. P.G. Surkov, Tracking of solutions to parabolic equations with memory in a general class of controls. Russian Math. 60 (2016) 44–54. [Google Scholar]
  26. N.D. Toan, Optimal control of nonclassical diffusion equations with memory. Acta Appl. Math. 169 (2020) 533–558. [CrossRef] [MathSciNet] [Google Scholar]
  27. J. Yong and X. Zhang, Heat equations with memory. Nonlinear Anal. 63 (2005) e99–e108. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.