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Motion of discrete interfaces in low-contrast periodic media
A note on the Trace Theorem for domains which are locally subgraph of a Hölder continuous function
1. | Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb |
References:
[1] |
R. A. Adams, Sobolev Spaces, Pure and Applied Mathematics, 65, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. |
[2] |
A. Chambolle, B. Desjardins, M. J. Esteban and C. Grandmont, Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate, J. Math. Fluid Mech., 7 (2005), 368-404.
doi: 10.1007/s00021-004-0121-y. |
[3] |
C. H. A. Cheng and S. Shkoller, The interaction of the 3D Navier-Stokes equations with a moving nonlinear Koiter elastic shell, SIAM J. Math. Anal., 42 (2010), 1094-1155.
doi: 10.1137/080741628. |
[4] |
S. Čanić and B. Muha, A nonlinear moving-boundary problem of parabolic-hyperbolic-hyperbolic type arising in fluid-multi-layered structure interaction problems, to appear in Proceedings of the Fourteenth International Conference on Hyperbolic Problems: Theory, Numerics and Applications, American Institute of Mathematical Sciences (AIMS) Publications. |
[5] |
Z. Ding, A proof of the trace theorem of Sobolev spaces on Lipschitz domains, Proc. Amer. Math. Soc., 124 (1996), 591-600.
doi: 10.1090/S0002-9939-96-03132-2. |
[6] |
C. Grandmont, Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate, SIAM J. Math. Anal., 40 (2008), 716-737.
doi: 10.1137/070699196. |
[7] |
P. Grisvard, Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics, 24, Pitman (Advanced Publishing Program), Boston, MA, 1985. |
[8] |
I. Kukavica and A. Tuffaha, Solutions to a fluid-structure interaction free boundary problem, DCDS-A, 32 (2012), 1355-1389.
doi: 10.3934/dcds.2012.32.1355. |
[9] |
D. Lengeler and M. Ružička, Weak solutions for an incompressible newtonian fluid interacting with a linearly elastic koiter shell, Arch. Ration. Mech. Anal., 211 (2014), 205-255.
doi: 10.1007/s00205-013-0686-9. |
[10] |
J. Lequeurre, Existence of strong solutions for a system coupling the Navier-Stokes equations and a damped wave equation, J. Math. Fluid Mech., 15 (2013), 249-271.
doi: 10.1007/s00021-012-0107-0. |
[11] |
J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications. Vol. I, Translated from the French by P. Kenneth, Die Grundlehren der mathematischen Wissenschaften, Band 181, Springer-Verlag, New York, 1972. |
[12] |
B. Muha and S. Čanić, Existence of a weak solution to a nonlinear fluid-structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls, Arch. Ration. Mech. Anal., 207 (2013), 919-968.
doi: 10.1007/s00205-012-0585-5. |
[13] |
B. Muha and S. Čanić, Existence of a solution to a fluid-multi-layered-structure interaction problem, J. of Diff. Equations, 256 (2014), 658-706.
doi: 10.1016/j.jde.2013.09.016. |
show all references
References:
[1] |
R. A. Adams, Sobolev Spaces, Pure and Applied Mathematics, 65, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. |
[2] |
A. Chambolle, B. Desjardins, M. J. Esteban and C. Grandmont, Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate, J. Math. Fluid Mech., 7 (2005), 368-404.
doi: 10.1007/s00021-004-0121-y. |
[3] |
C. H. A. Cheng and S. Shkoller, The interaction of the 3D Navier-Stokes equations with a moving nonlinear Koiter elastic shell, SIAM J. Math. Anal., 42 (2010), 1094-1155.
doi: 10.1137/080741628. |
[4] |
S. Čanić and B. Muha, A nonlinear moving-boundary problem of parabolic-hyperbolic-hyperbolic type arising in fluid-multi-layered structure interaction problems, to appear in Proceedings of the Fourteenth International Conference on Hyperbolic Problems: Theory, Numerics and Applications, American Institute of Mathematical Sciences (AIMS) Publications. |
[5] |
Z. Ding, A proof of the trace theorem of Sobolev spaces on Lipschitz domains, Proc. Amer. Math. Soc., 124 (1996), 591-600.
doi: 10.1090/S0002-9939-96-03132-2. |
[6] |
C. Grandmont, Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate, SIAM J. Math. Anal., 40 (2008), 716-737.
doi: 10.1137/070699196. |
[7] |
P. Grisvard, Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics, 24, Pitman (Advanced Publishing Program), Boston, MA, 1985. |
[8] |
I. Kukavica and A. Tuffaha, Solutions to a fluid-structure interaction free boundary problem, DCDS-A, 32 (2012), 1355-1389.
doi: 10.3934/dcds.2012.32.1355. |
[9] |
D. Lengeler and M. Ružička, Weak solutions for an incompressible newtonian fluid interacting with a linearly elastic koiter shell, Arch. Ration. Mech. Anal., 211 (2014), 205-255.
doi: 10.1007/s00205-013-0686-9. |
[10] |
J. Lequeurre, Existence of strong solutions for a system coupling the Navier-Stokes equations and a damped wave equation, J. Math. Fluid Mech., 15 (2013), 249-271.
doi: 10.1007/s00021-012-0107-0. |
[11] |
J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications. Vol. I, Translated from the French by P. Kenneth, Die Grundlehren der mathematischen Wissenschaften, Band 181, Springer-Verlag, New York, 1972. |
[12] |
B. Muha and S. Čanić, Existence of a weak solution to a nonlinear fluid-structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls, Arch. Ration. Mech. Anal., 207 (2013), 919-968.
doi: 10.1007/s00205-012-0585-5. |
[13] |
B. Muha and S. Čanić, Existence of a solution to a fluid-multi-layered-structure interaction problem, J. of Diff. Equations, 256 (2014), 658-706.
doi: 10.1016/j.jde.2013.09.016. |
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