Publication Cover
Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 13
55
Views
0
CrossRef citations to date
0
Altmetric
Articles

Nonlinear evolution equations with noncoercive lower order terms

, &
Pages 4615-4638 | Received 28 Feb 2020, Accepted 04 Dec 2020, Published online: 29 Dec 2020

References

  • Diperna RJ. On the cauchy problem for the Boltzmann equations: global existence and weak stability. Ann Math. 1989;130:285–366.
  • Blanchard D, Murat F. Renormalized solutions of nonlinear parabolic with L1 data: existence and uniqueness. Proc Roy Soc Edinburgh Sect A. 1997;127:137–152.
  • Boccardo L, Giachetti D, Diaz-Ildefonso J, et al. Existence and regularity of renormalized solutions of some elliptic problems involving derivatives of nonlinear terms. J Differ Equ. 1993;106:215–237.
  • Dal Maso G, Murat F, Orsina L, et al. Renormalized solutions of elliptic equations with general measure data. Ann Scuala Norm Sup Pisa Cl.Sci. 1999;28:241–273.
  • Del Vecchio T, Postraro R. An existence result for nonlinear and noncoercive problems. Nonlinear Anal. 1998;31:191–206.
  • Di Nardo R, Feo F, Guibè O. Existence result for nonlinear parabolic equations with lower order terms. Anal Appl Singap. 2011;2:161–186.
  • Aberqi A, Bennouna J, Mekkour M, et al. Renormalized solution for a nonlinear parabolic equation with lower order terms. Australian J Math Anal Appl. 2013;10:1–15.
  • Aberqi A, Bennouna J, Hammoumi M. Uniqueness of renormalized solutions for a class of parabolic equations. Ricerche Matematica. 2017;66:629–644.
  • Bendahmane M, Zimmermann A. Renormalized solutions for a nonlinear parabolic equation with variable exponents and L1-data. J Differ Equ. 2010;6:483–515.
  • Bendahmane M, Wittbold P. Renormalized solutions for nonlinear elliptic equations with variable exponents and L1data. Nonlinear Anal. 2009;2:567–583.
  • Chen Y, Levine S, Rao M. Functionals with p(x)-growth in image processing, Duquesne University, Department of Mathematics and Computer Science Technical Report 04-01. Available from: www.mathcs.duq.edu/sel/CLR05SIAPfinal.pdf.
  • Ruzicka M. Electrorheological fluids: modeling and mathematical theory. Berlin: Springer-Verlag; 2000.
  • Diening L. Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces Lp(.) and Wk,p(.). Math Nachr. 2004;268:31–43.
  • Fan X, Zhao D. On the spaces Lp(x)(U) and Wm,p(x)(U). J Math Anal Appl. 2001;263:424–446.
  • Zhikov-Vasilii V. On the density of smooth functions in Sobolev-Orlicz spaces. Zap Nauchn Sem S-Peterburg Otdel Mat Inst Steklov. 2004;310:67–81.
  • Almeida A, Hasto P. Besov spaces with variable smoothness and integrability. J Funct Anal. 2010;5:162–165.
  • Porretta A. Existence results for nonlinear parabolic equations via strong convergence of truncations. Ann Mat Pura ed Applicata. 1999;177:143–172.
  • Lions JL. Quelques méthodes de résolutions des problèmes aux limites non linéaires. Paris: Dunod et Gauthier-Villars; 1969.
  • Bennouna J, El Hamdaoui B, Mekkour M, et al. Nonlinear parabolic inequalities in Lebesgue-Sobolev spaces with variable exponent. Ricerche Matematica. 2016;65:93–125.
  • Blanchard F, Redwane H. Renormalized solutions for class of nonlinear evolution problems. J Math Pure. 1998;77:117–151.
  • Landes R. On the existence of weak solutions for quasilinear parabolic initial-boundary problems. Proc Roy Soc Edinburgh Sect. 1981;89:321–366.
  • Blanchard D, Murat F, Redwane H. Existence and uniqueness of renormalized solution for fairly general class of nonlinear parabolic problems. J Differ Equ. 2001;177:331–374.
  • Redwane H. Existence of solution for a class of a parabolic equation with three unbounded nonlinearities. Adv Dyn Syt. 2007;2:241–264.
  • Simon J. Compact set in the space Lp(0,T,B). Ann Mat Pura Appl. 1987;146:65–96.

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.