Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 5
134
Views
0
CrossRef citations to date
0
Altmetric
Research Article

The initial-nonlinear nonlocal solutions for a parabolic system in a weighted Sobolev space

ORCID Icon & ORCID Icon
Pages 1364-1393 | Received 13 Apr 2020, Accepted 16 Sep 2021, Published online: 01 Oct 2021

References

  • Ngoc LTP, Nhan TT, Thuyet TM, et al. On the nonlinear pseudoparabolic equation with the mixed inhomogeneous condition. Boundary Value Probl. 2016;2016:137.
  • Cordier S, Truong LX, Long NT, et al. Large time behavior of differential equations with drifted periodic coefficients modeling carbon storage in soil. Appl Math Comput. 2012;218(9):5641–5654.
  • Alexandre R, Dinh APN, Simon A, et al. A mathematical model for the evaporation of a liquid fuel droplet inside an infinite vessel. Nonlinear Anal Appl. 2003;1:117–140.
  • Alexandre R, Long NT, Dinh APN. A mathematical model for the evaporation of a liquid fuel droplet, subject to nonlinear constraints. Appl Math Comput. 2008;199:139–154.
  • Brezis H. Functional analysis, Sobolev spaces and partial differential equations. New York: Springer Science & Business Media; 2010.
  • Kubica A, Zajaczkowski WM. A parabolic system in a weighted Sobolev space. Appl Math. 2007;34(2):169–191.
  • Lauerova D. The existence of a periodic solution of a parabolic equation with the Bessel operator. Apl Mat. 1984;29(1):40–44.
  • Long NT, Dinh APN. Periodic solutions of a nonlinear parabolic equation involving Bessel's operator. Comput Math Appl. 1993;25:11–18.
  • Wang G, Liu C. The heat equation in R with anti-periodic boundary condition. Acta Math Sci. 1999;19:391–401.
  • Long NT, Dinh APN. On a nonlinear parabolic equation involving Bessel's operator associated with a mixed inhomogeneous condition. J Comput Appl Math. 2006;196:267–284.
  • Minasjan RS. On one problem of the periodic heat flow in the infinite cylinder. Dokl. Akad. Nauk. Arm. SSR. 1969;48.
  • Sirignano W. Fluid dynamics and transport of droplets and sprays. Cambridge: Cambridge University Press; 1999.
  • Aizicovici S, McKibben S, Reich S. Anti-periodic solutions to non-monotone evolution equations with discontinuous nonlinearities. Nonlinear Anal TMA. 2001;43:233–251.
  • Franco D, Nieto JJ, O'Regan D. Anti-periodic boundary value problem for nonlinear first order ordinary differential equations. J Math Inequal Appl. 2003;6:477–485.
  • Franco D, Nieto JJ, O'Regan D. Existence of solutions for first order ordinary differential equations with nonlinear boundary conditions. Appl Math Comput. 2004;153:793–802.
  • Liu Z. Anti-periodic solutions to nonlinear evolution equations. J Funct Anal. 2010;258:196–207.
  • Adams RA. Sobolev spaces. New York: Academic Press; 1975.
  • Efendiev M. Symmetrization and stabilization of nonlinear elliptic equations. Cham: Springer; 2018. p. 258.
  • Evans LC. Partial differential equations. 2nd ed. Providence, RI: Graduate Studies in Mathematics, American Mathematical Society; 2010. p. 749.
  • Kufner A, Opic B. How to define reasonably weighted Sobolev spaces. Comment Math Univ Carolinae. 1984;25(3):537–554.
  • Lions JL. Quelques méthodes de résolution des problèmes aux limites nonlinéaires. Paris: Dunod, Gauthier-Villars; 1969.
  • Long NT, Dinh APN. Periodic solutions of a nonlinear parabolic equation associated with the penetration of a magnetic field into a substance. Comput Math Appl. 1995;30:63–78.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.