Équations de réaction-diffusion sur des domaines minces d'épaisseur non uniforme. Un problème de Navier-Stokes à frontière libre
Thèses d'Orsay, no. 406 (1995) , 174 p. 
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     author = {Ciuperca, Lionel},
     title = {\'Equations de r\'eaction-diffusion sur des domaines minces d'\'epaisseur non uniforme. {Un} probl\`eme de {Navier-Stokes} \`a fronti\`ere libre},
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     year = {1995},
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Ciuperca, Lionel. Équations de réaction-diffusion sur des domaines minces d'épaisseur non uniforme. Un problème de Navier-Stokes à frontière libre. Thèses d'Orsay, no. 406 (1995), 174 p. http://numdam.org/item/BJHTUP11_1995__0406__P0_0/

[1] M. Abounouh, Thèse de troisième cycle, Orsay, 1993.

[2] J. M. Arrieta, Spectral properties of Schrödinger Operators under perturbations of the domains, Doctoral disertation, September 1991, Georgia Institute of Technology. | MR

[3] J. M. Arrieta, Neumann eigenvalues problems on exterior perturbation of the domain, - preprint. | MR | Zbl

[4] J. M. Arrieta, Rates of eigenvalues on a dumbbell domain. Simple eigenvalues case, - submitted to Transactions of A.M.S. | MR | Zbl

[5] S. N. Chow and K. Lu, Invariant Manifolds for Flows in Banach Spaces, Journal of diff. equations, 74 (1988) pp. 285-317. | MR | Zbl | DOI

[6] A. Debusche and R. Temam, Inertial Manifolds and the slow manifolds in meteorology, Differential and Integral Equations, Volume 4, Number 5, Septembre 1991 , pp. 897-931. | MR | Zbl

[7] C. Foias and R. Temam, Structure of the Set of Stationary Solutions of the Navier-Stokes Equations, Comm. Pure Appl. Math., Vol XXX (1977) pp. 149-164. | MR | Zbl | DOI

[8] J. K. Hale, Asymptotic Behavior of Dissipative Systems, Math. Surveys and Monographs 25 (1988) Am. Math. Soc. | MR | Zbl

[9] J. K. Hale and G. Raugel, Partial differential equations on thin domains, - preprint. | MR | Zbl

[10] J. K. Hale and G. Raugel, Reaction-diffusion equation on thin domains, J. Math. Pures Appl., 71 (1992), 33-95. | MR | Zbl

[11] J. K. Hale and G. Raugel, Convergence in Gradient-like Systems with applications to P.D.E, Z angew Math. Phys, 43 (1992), p. 63-124. | MR | Zbl

[12] J. K. Hale and G. Raugel, A damped hyperbolic equation on thin domain, Transactions of the A.M.S, Vol. 329, Number 1, January 1992, pp. 185-219. | MR | Zbl | DOI

[13] J. K. Hale and G. Raugel, A reaction-diffusion equation on a thin L-shaped domain - preprint. | MR | Zbl

[14] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lect. Notes Math., 840 (1981) , Springer-Verlag, Berlin. | MR | Zbl

[15] S. Jimbo, Singular Perturbation of Domains and semilinear elliptic equation, J. Fac. Sci. Univ. Tokyo, Sect. IA, Math 35 (1988), pp. 27-76. | MR | Zbl

[16] S. Jimbo, The Singularly Perturbed Domains and the characterization for the eigenfunctions with Neumann Boundary Condition, Journal of Differential Equations, 77, 322 - 350 (1989). | MR | Zbl | DOI

[17] S. Jimbo, A construction of the perturbed solution of semilinear elliptic equation in the singularly perturbed domain, J. Fac. Sci. Univ. Tokyo, Sect. IA, Math 36 (1989) no. 2, pp. 163 - 185. | MR | Zbl

[18] T. Kato, Perturbation Theory for Linear Operators, 2-nd Edition, Springer Verlag, Berlin Heidelberg New-York, 1976 | MR | Zbl

T. Kato, Problèmes aux limites non homogènes et applications, Dunod, Paris, 1968.

[19] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam, 1977. | Zbl | MR

[1] S. Agmon, A. Douglis, and L. Nirenberg, Estimations near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II, Comm. Pure Appl. Math. Vol 17 , (1964), p. 35-92. | MR | Zbl | DOI

[2] G. Allain, Un problème de Navier-Stokes avec surface libre et tension superficielle, Annales Faculté des Sciences Toulouse Vol VII, (1985), p. 29-56. | MR | Zbl | Numdam | DOI

[3] T. Beale, The initial value problem for the Navier-Stokes Equations with a free surface, Comm. Pure Appl. Math. 34, (1980), p. 359-392. | MR | Zbl | DOI

[4] A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New-York, 1969. | MR | Zbl

[5] O. A. Ladyzhenskaya, The mathematical Theory of Viscous Incompressible flow, Second Ed, Gordon and Breach, New-York, 1969. | MR | Zbl

[6] J. L. Lions and E. Magenes, Problèms aux limites non homogènes et applications, Dunod, Paris, 1968. | Zbl

[7] V. A. Solonnikov and V. E. Skadilov, On a boundary value problem on a stationary system of Navier-Stokes equations, Proc. Steklov Inst. Math., 15, (1973), p. 186-199. | Zbl

[8] V. A. Solonnikov, The solvability of the second initial value problem of the linear, time-dependent system of Navier-Stokes equations, J. Soviet Math. 10, (1978), p. 141-155. | Zbl | DOI

[9] V. A. Solonnikov, On the transient motion of an isolated volume of viscous incompressible fluid, Math. USSR Izvestiya, Vol 31 (1988), No. 2. | Zbl | MR

[10] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam, 1977. | Zbl | MR