Spatial decay estimates for the Forchheimer fluid equations in a semi-infinite cylinder

Xuejiao Chen; Yuanfei Li

Applications of Mathematics (2023)

  • Volume: 68, Issue: 5, page 643-660
  • ISSN: 0862-7940

Abstract

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The spatial behavior of solutions is studied in the model of Forchheimer equations. Using the energy estimate method and the differential inequality technology, exponential decay bounds for solutions are derived. To make the decay bounds explicit, we obtain the upper bound for the total energy. We also extend the study of spatial behavior of Forchheimer porous material in a saturated porous medium.

How to cite

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Chen, Xuejiao, and Li, Yuanfei. "Spatial decay estimates for the Forchheimer fluid equations in a semi-infinite cylinder." Applications of Mathematics 68.5 (2023): 643-660. <http://eudml.org/doc/299571>.

@article{Chen2023,
abstract = {The spatial behavior of solutions is studied in the model of Forchheimer equations. Using the energy estimate method and the differential inequality technology, exponential decay bounds for solutions are derived. To make the decay bounds explicit, we obtain the upper bound for the total energy. We also extend the study of spatial behavior of Forchheimer porous material in a saturated porous medium.},
author = {Chen, Xuejiao, Li, Yuanfei},
journal = {Applications of Mathematics},
keywords = {spatial behavior; Forchheimer equations; energy estimate bounds; upper bound; porous medium},
language = {eng},
number = {5},
pages = {643-660},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Spatial decay estimates for the Forchheimer fluid equations in a semi-infinite cylinder},
url = {http://eudml.org/doc/299571},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Chen, Xuejiao
AU - Li, Yuanfei
TI - Spatial decay estimates for the Forchheimer fluid equations in a semi-infinite cylinder
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 5
SP - 643
EP - 660
AB - The spatial behavior of solutions is studied in the model of Forchheimer equations. Using the energy estimate method and the differential inequality technology, exponential decay bounds for solutions are derived. To make the decay bounds explicit, we obtain the upper bound for the total energy. We also extend the study of spatial behavior of Forchheimer porous material in a saturated porous medium.
LA - eng
KW - spatial behavior; Forchheimer equations; energy estimate bounds; upper bound; porous medium
UR - http://eudml.org/doc/299571
ER -

References

top
  1. Boley, B. A., 10.2514/8.3503, J. Aeronaut. Sci. 23 (1956), 67-75. (1956) Zbl0070.18903DOI10.2514/8.3503
  2. Chen, W., 10.4310/CMS.2020.v18.n2.a7, Commun. Math. Sci. 18 (2020), 429-457. (2020) Zbl1472.35048MR4101316DOI10.4310/CMS.2020.v18.n2.a7
  3. Chen, W., 10.3233/ASY-191548, Asymptotic Anal. 117 (2020), 113-140. (2020) Zbl1467.35048MR4158328DOI10.3233/ASY-191548
  4. Chen, X., Li, Y., Li, D., 10.3390/sym14010098, Symmetry 14 (2022), Article ID 98, 22 pages. (2022) DOI10.3390/sym14010098
  5. Saint-Venant, A. J. B. De, Mémoire sur la flexion des prismes, J. Math. Pures Appl. (2) 1 (1856), 89-189 French. (1856) 
  6. Firdaouss, M., Guermond, J.-L., Quéré, P. Le, 10.1017/S0022112097005843, J. Fluid Mech. 343 (1997), 331-350. (1997) Zbl0897.76091MR1465159DOI10.1017/S0022112097005843
  7. Franchi, F., Straughan, B., 10.1098/rspa.2003.1169, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 459 (2003), 3195-3202. (2003) Zbl1058.35030MR2027361DOI10.1098/rspa.2003.1169
  8. Gentile, M., Straughan, B., 10.1016/j.nonrwa.2012.07.003, Nonlinear Anal., Real World Appl. 14 (2013), 397-401. (2013) Zbl1254.76142MR2969842DOI10.1016/j.nonrwa.2012.07.003
  9. Giorgi, T., 10.1023/A:1006533931383, Transp. Porous Media 29 (1997), 191-206. (1997) DOI10.1023/A:1006533931383
  10. Horgan, C. O., 10.1115/1.3152414, Appl. Mech. Rev. 42 (1989), 295-302. (1989) MR1021553DOI10.1115/1.3152414
  11. Horgan, C. O., 10.1115/1.3101961, Appl. Mech. Rev. 49 (1996), S101--S111. (1996) MR1021553DOI10.1115/1.3101961
  12. Horgan, C. O., Knowles, J. K., 10.1016/S0065-2156(08)70244-8, Adv. Appl. Mech. 23 (1983), 179-269. (1983) Zbl0569.73010MR0889288DOI10.1016/S0065-2156(08)70244-8
  13. Horgan, C. O., Payne, L. E., 10.1007/BF00378164, Arch. Ration. Mech. Anal. 122 (1993), 123-144. (1993) Zbl0790.31002MR1217587DOI10.1007/BF00378164
  14. Knops, R. J., Quintanilla, R., 10.1007/s10659-015-9523-8, J. Elasticity 121 (2015), 89-117. (2015) Zbl1326.35376MR3394434DOI10.1007/s10659-015-9523-8
  15. Knops, R. J., Quintanilla, R., 10.1090/qam/1497, Q. Appl. Math. 76 (2018), 611-625. (2018) Zbl1397.58010MR3855824DOI10.1090/qam/1497
  16. Knowles, J. K., 10.1007/BF00253046, Arch. Ration. Mech. Anal. 21 (1966), 1-22. (1966) MR0187480DOI10.1007/BF00253046
  17. Knowles, J. K., An energy estimate for the biharmonic equation and its application to Saint-Venant's principle in plane elastostatics, Indian J. Pure Appl. Math. 14 (1983), 791-805. (1983) Zbl0524.73001MR0714832
  18. Leseduarte, M. C., Quintanilla, R., 10.11948/2017081, J. Appl. Anal. Comput. 7 (2017), 1323-1335. (2017) Zbl1447.35085MR3723923DOI10.11948/2017081
  19. Li, Y., Chen, X., 10.1002/mma.8220, Math. Methods Appl. Sci. 45 (2022), 6982-6997. (2022) MR4443365DOI10.1002/mma.8220
  20. Li, Y., Chen, X., Shi, J., 10.1007/s00245-021-09791-7, Appl. Math. Optim. 84 (2021), S979--S999. (2021) Zbl1477.35173MR4316807DOI10.1007/s00245-021-09791-7
  21. Li, Y., Xiao, S., 10.21136/AM.2021.0076-20, Appl. Math., Praha 67 (2022), 103-124. (2022) Zbl07478520MR4392408DOI10.21136/AM.2021.0076-20
  22. Li, Y., Xiao, S., Zeng, P., 10.7153/jmi-2021-15-22, J. Math. Inequal. 15 (2021), 293-304. (2021) Zbl1465.35018MR4364642DOI10.7153/jmi-2021-15-22
  23. Li, Y., Zeng, P., 10.3390/sym13101961, Symmetry 13 (2021), Article ID 1961, 16 pages. (2021) DOI10.3390/sym13101961
  24. Lin, C., 10.7153/mia-09-60, Acta Math. Sci. 16 (1996), 181-191. (1996) Zbl0866.35041MR1402960DOI10.7153/mia-09-60
  25. Liu, Y., 10.1016/j.amc.2017.03.004, Appl. Math. Comput. 308 (2017), 18-30. (2017) Zbl1411.35228MR3638153DOI10.1016/j.amc.2017.03.004
  26. Liu, Y., Lin, C., 10.7153/mia-09-60, Math. Inequal. Appl. 9 (2006), 671-694. (2006) Zbl1116.35021MR2268176DOI10.7153/mia-09-60
  27. Liu, Y., Lin, Y., Li, Y., 10.1016/j.aml.2012.04.001, Appl. Math. Lett. 26 (2013), 97-102. (2013) Zbl1252.74014MR2971407DOI10.1016/j.aml.2012.04.001
  28. Liu, Y., Qin, X., Shi, J., Zhi, W., 10.1016/j.amc.2021.126488, Appl. Math. Comput. 411 (2021), Article ID 126488, 10 pages. (2021) Zbl07426871MR4284432DOI10.1016/j.amc.2021.126488
  29. Liu, Y., Xiao, S., Lin, Y., 10.1016/j.matcom.2018.02.009, Math. Comput. Simul. 150 (2018), 66-82. (2018) Zbl07316235MR3783079DOI10.1016/j.matcom.2018.02.009
  30. Liverani, L., Quintanilla, R., 10.1177/10812865221115359, (to appear) in Math. Mech. Solids. MR4574895DOI10.1177/10812865221115359
  31. Néel, M.-C., 10.1016/S1251-8069(98)89004-0, C. R. Acad. Sci., Paris, Sér. II, Fasc. b, Méc. Phys. Astron. 326 (1998), 615-620 French. (1998) Zbl0915.76086DOI10.1016/S1251-8069(98)89004-0
  32. Payne, L. E., Schaefer, P. W., 10.1007/BF00945929, Z. Angew. Math. Phys. 45 (1994), 414-432. (1994) Zbl0810.31001MR1278684DOI10.1007/BF00945929
  33. Payne, L. E., Song, J. C., 10.1016/S0020-7225(01)00102-1, Int. J. Eng. Sci. 40 (2002), 943-956. (2002) Zbl1211.76119DOI10.1016/S0020-7225(01)00102-1
  34. Payne, L. E., Straughan, B., 10.1016/S0021-7824(98)80102-5, J. Math. Pures Appl., IX. Sér. 77 (1998), 317-354. (1998) Zbl0906.35067MR1623387DOI10.1016/S0021-7824(98)80102-5
  35. Payne, L. E., Straughan, B., 10.1111/1467-9590.00116, Stud. Appl. Math. 102 (1999), 419-439. (1999) Zbl1136.76448MR1684989DOI10.1111/1467-9590.00116
  36. Payne, L. E., Straughan, B., 10.1111/1467-9590.00142, Stud. Appl. Math. 105 (2000), 59-81. (2000) Zbl1136.35318MR1856630DOI10.1111/1467-9590.00142
  37. Quintanilla, R., 10.1007/s00033-019-1127-x, Z. Angew. Math. Phys. 70 (2019), Article ID 83, 18 pages. (2019) Zbl1415.35070MR3948948DOI10.1007/s00033-019-1127-x
  38. Quintanilla, R., Racke, R., Spatial behavior in phase-lag heat conduction, Differ. Integral Equ. 28 (2015), 291-308. (2015) Zbl1363.35236MR3306564
  39. Shi, J., Liu, Y., 10.1186/s13661-021-01525-6, Bound. Value Probl. 2021 (2021), Article ID 46, 22 pages. (2021) Zbl07509890MR4252231DOI10.1186/s13661-021-01525-6
  40. Straughan, B., 10.1007/978-0-387-21740-6, Applied Mathematical Sciences 91. Springer, New York (2004). (2004) Zbl1032.76001MR2003826DOI10.1007/978-0-387-21740-6
  41. Straughan, B., 10.1111/j.1467-9590.2011.00521.x, Stud. Appl. Math. 127 (2011), 302-314. (2011) Zbl1250.80001MR2852484DOI10.1111/j.1467-9590.2011.00521.x
  42. Straughan, B., 10.1007/s10652-022-09888-9, Environmental Fluid Mech. 22 (2022), 1233-1252. (2022) DOI10.1007/s10652-022-09888-9

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