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Tytuł artykułu

On the solvability of some parabolic equations involving nonlinear boundary conditions with L1 data

Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We analyze the existence of solutions for a class of quasilinear parabolic equations with critical growth nonlinearities, nonlinear boundary conditions, and L1 data. We formulate our problems in an abstract form, then using some techniques of functional analysis, such as Leray-Schauder’s topological degree associated with the truncation method and very interesting compactness results, we establish the existence of weak solutions to the proposed models.
Rocznik
Strony
587--623
Opis fizyczny
Bibliogr. 32 poz.
Twórcy
  • Ibn Zohr University, Higher School of Education and Training of Agadir, New University Complex, Agadir, 80000, Morocco
  • Interdisciplinary Research Laboratory in Sciences, Education and Training, Higher School of Education and Training of Berrechid (ESEFB), Hassan First University, Morocco
  • Laboratory LAMAI, Faculty of Science and Technology of Marrakech, B.P. 549, Av. Abdelkarim Elkhattabi, 40000, Marrakech, Morocco
Bibliografia
  • [1] H. Alaa, N.E. Alaa, A. Charkaoui, Time periodic solutions for strongly nonlinear parabolic systems with p(x)-growth conditions, J. Elliptic Parabol. Equ. 7 (2021), 815–839.
  • [2] H. Alaa, M. El Ghabi, A. Charkaoui, Semilinear periodic parabolic problem with discontinuous coefficients: Mathematical analysis and numerical simulation, Filomat 37 (2023), no. 7, 2151–2164.
  • [3] N.E. Alaa, F. Aqel, L. Taourirte, On singular quasilinear elliptic equations with data measures, Adv. Nonlinear Anal. 10 (2021), 1284–1300.
  • [4] N.E. Alaa, A. Charkaoui, M. El Ghabi, M. El Hathout, Integral solution for a parabolic equation driven by the p(x)-Laplacian operator with nonlinear boundary conditions and L1 data, Mediterr. J. Math. 20 (2023), Article no. 244.
  • [5] H. Amann, Nonlinear elliptic equations with nonlinear boundary conditions, North-Holland Mathematics Studies 21 (1976), 43–63.
  • [6] P. Amster, Topological methods for a nonlinear elliptic system with nonlinear boundary conditions, Int. J. Dyn. Syst. Differ. Equ. 2 (2009), no. 1–2, 56–65.
  • [7] P. Amster, Multiple solutions for an elliptic system with indefinite Robin boundary conditions, Adv. Nonlinear Anal. 8 (2017), no. 1, 603–614.
  • [8] F. Andreu, J.M. Mazón, S. Segura de León, J. Toledo, Quasi-linear elliptic and parabolic equations in L1 with nonlinear boundary conditions, Adv. Math. Sci. Appl. 7 (1997), 183–213.
  • [9] P. Baras, M. Pierre, Problèmes paraboliques semi-lineaires avec donnees measures, Appl. Anal. 18 (1984), no. 1–2, 111–149.
  • [10] D. Bothe, M. Pierre, Quasi-steady-state approximation for a reaction–diffusion system with fast intermediate, J. Math. Anal. Appl. 368 (2010), no. 1, 120–132.
  • [11] A. Cabada, R.L. Pouso, Existence results for the problem (ϕ(u)) = f(t, u,∇u) with nonlinear boundary conditions, Nonlinear Anal. 35 (1999), no. 2, 221–231.
  • [12] A. Charkaoui, N.E. Alaa, Weak periodic solution for semilinear parabolic problem with singular nonlinearities and L1 data, Mediterr. J. Math. 17 (2020), Article no. 108.
  • [13] A. Charkaoui, N.E. Alaa, Existence and uniqueness of renormalized periodic solution to a nonlinear parabolic problem with variable exponent and L1 data, J. Math. Anal. Appl. 506 (2022), no. 2, Article no. 125674.
  • [14] A. Charkaoui, N.E. Alaa, An L1-theory for a nonlinear temporal periodic problem involving p(x)-growth structure with a strong dependence on gradients, J. Evol. Equ. 23 (2023), Article no. 73.
  • [15] A. Charkaoui, H. Fahim, N.E. Alaa, Nonlinear parabolic equation having nonstandard growth condition with respect to the gradient and variable exponent, Opuscula Math. 41 (2021), no. 1, 25–53.
  • [16] F.C.Ş. Cîrstea, V. Rădulescu, Existence and non-existence results for a quasilinear problem with nonlinear boundary condition, J. Math. Anal. Appl. 244 (2000), no. 1, 169–183.
  • [17] J. Droniou, Quelques résultats sur les espaces de Sobolev, Working paper or preprint, (2001).
  • [18] A. Elaassri, K. Lamrini Uahabi, A. Charkaoui, N.E. Alaa, S. Mesbahi, Existence of weak periodic solution for quasilinear parabolic problem with nonlinear boundary conditions, An. Univ. Craiova Ser. Mat. Inform. 46 (2019), 1–13.
  • [19] G.M. Figueiredo, V.D. Rădulescu, Nonhomogeneous equations with critical exponential growth and lack of compactness, Opuscula Math. 40 (2020), no. 1, 71–92.
  • [20] M. Fila, J. Lankeit, Lack of smoothing for bounded solutions of a semilinear parabolic equation, Adv. Nonlinear Anal. 9 (2020), no. 1, 1437–1452.
  • [21] J.L. Lions, Quelques méthodes de résolution de problèmes aux limites non linéaires, Dunod, 1969.
  • [22] C.B. Morrey, Multiple Integrals in the Calculus of Variations, Springer Science & Business Media, 2009.
  • [23] M. Nakao, Remarks on global solutions to the initial-boundary value problem for quasilinear degenerate parabolic equations with a nonlinear source term, Opuscula Math. 39 (2019), no. 3, 395–414.
  • [24] M. Niezgódka, I. Pawłow, A generalized Stefan problem in several space variables, Appl. Math. Optim. 9 (1982), 193–224.
  • [25] N. Papageorgiou, V. Rădulescu, D. Repov˘s, Nonlinear Analysis – Theory and Methods, Springer Monographs in Mathematics, 2019.
  • [26] A. Porretta, Existence results for nonlinear parabolic equations via strong convergence of truncations, Ann. Mat. Pura Appl. (4) 177 (1999), 143–172.
  • [27] A. Prignet, Existence and uniqueness of “entropy” solutions of parabolic problems with L1 data, Nonlinear Anal. 28 (1997), 1943–1954.
  • [28] V. Rădulescu, Nonlinear elliptic equations with variable exponent: old and new, Nonlinear Anal. 121 (2015), 336–369.
  • [29] V. Rădulescu, Isotropic and anisotropic double-phase problems: old and new, Opuscula Math. 39 (2019), 259–279.
  • [30] J.F. Rodrigues, The Stefan problem revisited, [in:] Mathematical Models for Phase Change Problems, Basel, Birkhäuser Basel, 1989, 129–190.
  • [31] J.F. Rodrigues, Variational methods in the Stefan problem, [in:] A. Visintin (ed.), Phase Transitions and Hysteresis, Springer, Berlin, 1994, 147–212.
  • [32] T. Roubíček, Nonlinear heat equation with L1-data, NoDEA Nonlinear Differential Equations Appl. 5 (1998), 517–527.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d5d7dfa6-a0a5-47e3-8faa-a3c0eb49e37f
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