Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 27
Number of page(s) 30
DOI https://doi.org/10.1051/cocv/2024016
Published online 09 April 2024
  1. L. Allen, B. Bolker, Y. Lou and N. Nevai, Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model. Disc. Cont. Dyn. Syst. 21 (2008) 1–20. [Google Scholar]
  2. A. Friedman, Partial Differential Equations of Parabolic Type. Dover Pub., Mineola, New York (2008). [Google Scholar]
  3. R. Peng, Asymptotic profiles of the positive steady state for an SIS epidemic reaction–diffusion model. Part I. J. Diff. Equ. 247 (2009) 1096–1119. [Google Scholar]
  4. Y. Wu and X. Zou, Asymptotic profiles of steady states for a diffusive SIS epidemic model with mass action infection mechanism. J. Diff. Equ. 261 (2016) 4424–4447. [Google Scholar]
  5. P. Albano and D. Tataru, Unique continuation for second-order parabolic operators at the initial time. Proc. Am. Math. Soc. 132 (2004) 1077–1085. [Google Scholar]
  6. H. Koch and D. Tataru, Carleman estimates and unique continuation for second order parabolic equations with nonsmooth coefficients. Commun. PDE 34 (2009) 305–366. [Google Scholar]
  7. K.D. Phung and G. Wang, Quantitative unique continuation for the semilinear heat equation in a convex domain. J. Funct. Anal. 259 (2010) 1230–1247. [Google Scholar]
  8. C. Poon, Unique continuation for parabolic equations. Commun. PDE 21 (1996) 521–539. [Google Scholar]
  9. G. Wang, M. Wang and Y. Zhang, Observability and unique continuation inequalities for the Schrödinger equation. J. Eur. Math. Soc. 21 (2019) 3513–3572. [Google Scholar]
  10. G. Zheng, D. Xu and T. Wang, A unique continuation property for a class of parabolic differential inequalities in a bounded domain. Commun. Pure Appl. Anal. 20 (2021) 547–558. [Google Scholar]
  11. J. Coron, Control and Nonlinearity. AMS Providence, Rhode Island (2007). [Google Scholar]
  12. X. Fu, J. Yong and X. Zhang, Controllability and observability of a heat equation with hyperbolic memory kernel. J. Diff. Equ. 247 (2009) 2395–2439. [Google Scholar]
  13. P. Lissy and E. Zuazua, Internal observability for coupled systems of linear partial differential equations. SIAM J. Control. Optim. 57 (2019) 832–853. [Google Scholar]
  14. Q. Lu, Observability estimate and state observation problems for stochastic hyperbolic equations. Inverse Probl. 29 (2013) Article 095011. [Google Scholar]
  15. Q. Lu, Observability estimate for stochastic Schrödinger equations and its applications. SIAM J. Control Optim. 51 (2013) 121–144. [Google Scholar]
  16. K.D. Phung and G. Wang, An observability estimate for parabolic equations from a measurable set in time and its applications. J. Eur. Math. Soc. 15 (2013) 681–703. [Google Scholar]
  17. K.D. Phung, Carleman commutator approach in logarithmic convexity for parabolic equations. Math. Control Relat. F 8 (2018) 899–933. [Google Scholar]
  18. F.J. Almgren Jr., Dirichlet’s problem for multiple valued functions and the regularity of mass minimizing integral currents, in Minimal Submanifolds and Geodesics. North-Holland, Amsterdam-New York (1979) 1–6. [Google Scholar]
  19. N. Garofalo and F. Lin, Monotonicity properties of variational integrals, Ap weights and unique continuation. Indiana Univ. Math. J. 35 (1986) 245–268. [Google Scholar]
  20. Q. Lü and Z. Yin, Unique continuation for stochastic heat equations. ESAIM Control Optim. Calc. Var. 21 (2015) 378–398. [Google Scholar]
  21. H. Brezis and T. Cazenave, A nonlinear heat equation with singular initial data. J. Anal. Math. 68 (1996) 277–304. [Google Scholar]
  22. T. Cazenave and A. Haraux, An Introduction to Semilinear Evolution Equations. Clarendon Press, Oxford (1998). [Google Scholar]
  23. J. Apraiz, L. Escauriaza, G. Wang and C. Zhang, Observability inequalities and measurable sets. J. Eur. Math. Soc. 16 (2014) 2433–2475. [Google Scholar]
  24. G. Wang and G. Zheng, Unique continuation inequalities for the parabolic-elliptic chemotaxis system. J. Diff. Equ. 317 (2022) 524–560. [Google Scholar]
  25. D. Daners, Heat kernal estimates for operators with boundary conditions. Math. Nachr. 217 (2000) 13–41. [Google Scholar]

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