We obtain the local well-posedness of a moving boundary problem that describes the swelling of a pocket of water within an infinitely thin elongated pore (i.e. on $ [a, +\infty), \ a>0 $). Our result involves fine a priori estimates of the moving boundary evolution, Banach fixed point arguments as well as an application of the general theory of evolution equations governed by subdifferentials.
|
Citation:
|
| [1] |
T. Aiki, Y. Murase, N. Sato and K. Shirakawa, A mathematical model for a hysteresis appearing in adsorption phenomena, SūrikaisekikenkyūshoKōkyūroku, 1856 (2013), 1-12.
|
| [2] |
T. Aiki and Y. Murase, On a large time behavior of a solution to a one-dimensional free boundary problem for adsorption phenomena, J. Math. Anal. Appl., 445 (2017), 837-854.
doi: 10.1016/j.jmaa.2016.06.008. |
| [3] |
T. Aiki and A. Muntean, Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structures, Adv. Math. Sci. Appl., 19 (2009), 109-129.
|
| [4] |
T. Aiki and A. Muntean, Large time behavior of solutions to a moving-interface problem modeling concrete carbonation, Comm. Pure Appl. Anal., 9 (2010), 1117-1129.
doi: 10.3934/cpaa.2010.9.1117. |
| [5] |
T. Aiki and A. Muntean, A free-boundary problem for concrete carbonation: Rigorous justification of $\sqrt{t}$–law of propagation, Interface. Free Bound., 15 (2013), 167-180.
doi: 10.4171/IFB/299. |
| [6] |
A. Fasano, G. Meyer and M. Primicerio, On a problem in the polymer industry: Theoretical and numerical investigation of swelling, SIAM J. Appl. Math., 17 (1986), 945-960.
doi: 10.1137/0517067. |
| [7] |
A. Fasano and A. Mikelic, The 3D flow of a liquid through a porous medium with adsorbing and swelling granules, Interface. Free Bound., 4 (2002), 239-261.
doi: 10.4171/IFB/60. |
| [8] |
T. Fatima, A. Muntean and T. Aiki, Distributed space scales in a semilinear reaction-diffusion system including a parabolic variational inequality: A well-posedness study, Adv. Math. Sci. Appl., 22 (2012), 295-318.
|
| [9] |
B. W. van de Fliert and R. van der Hout, A generalized Stefan problem in a diffusion model with evaporation, SIAM J. Appl. Math., 60 (2000), 1128-1136.
doi: 10.1137/S0036139997327599. |
| [10] |
A. Friedman and A. Tzavaras, A quasilinear parabolic system arising in modelling of catalytic reactors, J. Differential Equations, 70 (1987), 167-196.
doi: 10.1016/0022-0396(87)90162-8. |
| [11] |
N. Kenmochi, Solvability of nonlinear evolution equations with time-dependent constraints and applications, Bull. Fac. Education, Chiba Univ., 30 (1981), 1-87.
|
| [12] |
K. Kumazaki, T. Aiki, N. Sato and Y. Murase, Multiscale model for moisture transport with adsorption phenomenon in concrete materials, Appl. Anal., 97 (2018), 41-54.
doi: 10.1080/00036811.2017.1325473. |
| [13] |
K. Kumazaki and A. Muntean, Global weak solvability of a moving boundary problem describing swelling along a halfline, arXiv: 1810.08000.
|
| [14] |
A. Muntean and M. Böhm, A moving boundary problem for concrete carbonation: global existence and uniqueness of solutions, J. Math. Anal. Appl., 350 (2009), 234-251.
doi: 10.1016/j.jmaa.2008.09.044. |
| [15] |
A. Muntean and M. Neuss-Radu, A multiscale Galerkin approach for a class of nonlinear coupled reaction-diffusion systems in complex media, J. Math. Anal. Appl., 37 (2010), 705-718.
doi: 10.1016/j.jmaa.2010.05.056. |
| [16] |
T. L. van Noorden and I. S. Pop, A Stefan problem modelling crystal dissolution and precipitation, IMA J. Appl. Math., 73 (2008), 393-411.
doi: 10.1093/imamat/hxm060. |
| [17] |
T. L. van Noorden, I. S. Pop, A. Ebigbo and R. Helmig, An upscaled model for biofilm growth in a thin strip, Water Resour. Res., 46 (2010), 1-14.
doi: 10.1029/2009WR008217. |
| [18] |
N. Sato, T. Aiki, Y. Murase and K. Shirakawa, A one dimensional free boundary problem for adsorption phenomena, Netw. Heterog. Media, 9 (2014), 655-668.
doi: 10.3934/nhm.2014.9.655. |
| [19] |
M. J. Setzer, Micro-ice-lens formation in porous solid, J. Colloid Interface Sci., 243 (2001), 193-201.
doi: 10.1006/jcis.2001.7828. |
| [20] |
X. Weiqing, The Stefan problem with a kinetic condition at the free boundary, SIAM J. Math. Anal., 21 (1990), 362-373.
doi: 10.1137/0521020. |
| [21] |
M. Zaal, Cell swelling by osmosis: A variational approach, Interface. Free Bound., 14 (2012), 487-520.
doi: 10.4171/IFB/289. |