Approximations to precisely localized supports of solutions for non-linear parabolic p-Laplacian problems

• Autorzy: Jeli Roqia Abdullah

Identyfikatory

DOI

10.1515/dema-2024-0063

• Języki publikacji: EN

Abstrakty

EN

The shrinking of support in non-linear parabolic p-Laplacian equations with a positive initial condition 𝑢0 that decayed as ∣𝑥 ∣ →∞ was explored in the Cauchy problem. Proofs were provided for establishing exact local estimates for the boundary of the support of the solutions.

Słowa kluczowe

EN

local solution estimations; singular support behavior; support reduction; parabolic singularities; non-linear dynamics

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20240063
• Opis fizyczny: Bibliogr. 14 poz., tab.

Twórcy

autor

Jeli Roqia Abdullah

• Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia

Bibliografia

• [1] G. I. Barenblatt, On some unsteady motions of a liquid and gas in a porous medium, Prikl. Mat. Meh. 16 (1952), 67–78.
• [2] A. S. Kalashnikov, Some problems of the qualitative theory of second-order nonlinear degenerate parabolic equations, Uspekhi Mat. Nauk 42 (1987), no. 2, 135–176, 287.
• [3] U. G. Abdullaev, On sharp local estimates for the support of solutions in problems for nonlinear parabolic equations, Sb. Math. 186 (1995), no. 8, 1085–1106, DOI: https://doi.org/10.1070/SM1995v186n08ABEH000058.
• [4] L. K. Martinson and K. B. Pavlov, The problem of the three-dimensional localization of thermal perturbations in the theory of non-linear heat conduction, USSR Comput. Math. Math. Phys. 12 (1972), no. 4, 261–268, DOI: https://doi.org/10.1016/0041-5553(72)90131-0.
• [5] A. S. Kalašnikov, The nature of the propagation of perturbations in problems of nonlinear heat conduction with absorption, Z. Vycisl. Mat i Mat. Fiz. 14 (1974), 891–905, 1075.
• [6] L. C. Evans and B. F. Knerr, Instantaneous shrinking of the support of nonnegative solutions to certain nonlinear parabolic equations and variational inequalities, Illinois J. Math. 23 (1979), no. 1, 153–166, DOI: http://projecteuclid.org/euclid.ijm/1256048324.
• [7] M. A. Herrero, On the behavior of the solutions of certain nonlinear parabolic problems, Rev. R. Acad. Cienc. Exactas Fís. Nat. 75 (1981), no. 5, 1165–1183.
• [8] T. S. Khin and N. Su, Propagation property for nonlinear parabolic equations of p-Laplacian-type, Int. J. Math. Anal. 3 (2009), no. 9–12, 591–602.
• [9] D. Motreanu and E. Tornatore, Quasilinear Dirichlet problems with degenerated p-Laplacian and convection term, Mathematics 9 (2021), no. 2, 139.
• [10] P. Roselli and B. Sciunzi, A strong comparison principle for the p-Laplacian, Proc. Amer. Math. Soc. 135 (2007), no. 10, 3217–3224, DOI: https://doi.org/10.1090/S0002-9939-07-08847-8.
• [11] J. Yin and C. Wang, Evolutionary weighted p-Laplacian with boundary degeneracy, J. Differential Equations 237 (2007), no. 2, 421–445, DOI: https://doi.org/10.1016/j.jde.2007.03.012.
• [12] U. G. Abdulla and R. Jeli, Evolution of interfaces for the nonlinear parabolic p-Laplacian-type reaction-diffusion equations. II. Fast diffusion vs. absorption, European J. Appl. Math. 31 (2020), no. 3, 385–406, DOI: https://doi.org/10.1017/s095679251900007x.
• [13] Y. Han and W. Gao, Extinction of solutions to a class of fast diffusion systems with nonlinear sources, Math. Methods Appl. Sci. 39 (2016), no. 6, 1325–1335, DOI: https://doi.org/10.1002/mma.3571.
• [14] E. Di Benedetto, Degenerate Parabolic Equations, Springer-Verlag, New York, 1993.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2026).