Publication Cover
Applicable Analysis
An International Journal
Volume 87, 2008 - Issue 1
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Original Articles

Limit behaviour of optimal control problems governed by parabolic boundary value problems with equivalued surface

Pages 1-11 | Received 10 Jan 2007, Accepted 30 Sep 2007, Published online: 22 Jan 2008

References

  • Chen , ZX and Jiang , LS . 1980 . Exact solution for the system of flow equations through a medium with double-porosity . Scientia Sinica , 7 : 880 – 896 .
  • Damlamian , A and Li , TT . 1982 . Comportements limites des solutions de certains problèmes mixtes pour des équations paraboliques . Journal de Mathématiques Pures et Appliquées , 61 : 113 – 130 .
  • Damlamian , A and Li , TT . 1982 . Comportements limites des solutions de certains problèmes mixtes pour des équations paraboliques II . Acta Mathematica Scientia , 2 : 85 – 104 .
  • Ekeland , I and Temam , R . 1976 . Convex Analysis and Variational Problems , Amsterdam : North-Holland Publishing Company .
  • Li , FQ . 2000 . Limit behaviour of solutions to a class of equivalued surface boundary value problems for parabolic equations . Journal of Partial Differential Equations , 13 ( 2 ) : 111 – 122 .
  • Li , TT . 1989 . A class of non-local boundary value problems for partial differential equations and its applications in numerical analysis . Journal of Computational and Applied Mathematics , 28 : 49 – 62 .
  • Li , TT . 1980 . Comportements limites pour certains problèmes du contrôle optimal de systemes gouvernés par des équations paraboliques . Comptes rendus de l'Académie des Sciences , 291 : 201 – 204 .
  • Li , TT . 1982 . Limit behaviour of solutions for some parabolic equations of higher order and their applications to the optimal control . Chinese Annals of Mathematics , 3 ( 4 ) : 527 – 543 .
  • Li , TT , Zheng , SM , Tan , Y-J and Shen , W-X . 1998 . “ Boundary Value Problem with Equivalued Surface and The Resistivity Well-Logging ” . In Pitman Research Notes in Math Series , Vol. 382 , Essex : Longman .
  • Lions , JL . 1981 . Some Methods in the Mathematical Analysis of Systems and their Control , Beijing : Science Press .
  • Lions , JL . 1971 . Optimal Control of Systems Governed by Partial Differential Equations , Heidelberg : Springer-Verlag .
  • Lions , JL . 1969 . Quelques Méthodes de Résolution des Problémes aux Limites Nonlinéaires , Paris : Dunod, Gauthier–Villars .
  • Shen , W-X . 1978 . On mixed initial-boundary value problems of second order parabolic equations with equivalued surface boundary conditions (in Chinese) . Fudan Journal (Natural Science) , 4 : 15 – 24 .
  • Simon , J . 1987 . Compact sets in the space Lp(0, T; B) . Annali di Matematica Pura ed Applicata , 146 : 65 – 96 .

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