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Qualitative study for the p-Laplacian type diffusion-convection equation with the effect of an absorption source | ||
International Journal of Nonlinear Analysis and Applications | ||
مقاله 10، دوره 16، شماره 4، تیر 2025، صفحه 109-119 اصل مقاله (492.27 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.31245.4607 | ||
نویسندگان | ||
Habeeb Abed Aal-Rkhais* ؛ Dhuha K. Ajeel | ||
Department of Mathematics, College of Computer Science and Mathematics, Iraq | ||
تاریخ دریافت: 27 تیر 1402، تاریخ پذیرش: 21 مهر 1402 | ||
چکیده | ||
Within this paper, we study the initial growth of interfaces and asymptotic locally weak solutions by the construction of its self-similar solution to the Cauchy Problem for a parabolic p-Laplacian type diffusion-convection equation with the effect of absorption source. The significant methods are applied in this work, techniques of blowing up, rescaling, and comparison principles in non-smooth domains. The importance of this model came through its applications in a variety of fields such as chemical process design, biophysics, plasma physics, quantum physics, and others. | ||
کلیدواژهها | ||
p-Laplacian diffusion equation؛ rescaling technique؛ self-similarity؛ weak solution؛ interface | ||
مراجع | ||
[1] H.A. Aal-Rkhais and R.H. Qasim, The development of interfaces in a parabolic p-Laplacian type diffusion equation with weak convection, J. Phys.: Conf. Ser. IOP Pub. 963 (2021), no. 1. [2] U.G. Abdulla and R. Jeli, Evolution of interfaces for the non-linear parabolic p-Laplacian type reaction-diffusion equations, Eur. J. Appl. Math. 28 (2017), no. 5, 827–853. [3] U.G. Abdulla and R. Jeli, Evolution of interfaces for the nonlinear parabolic p-Laplacian-type reaction-diffusion equations. II. Fast diffusion vs. absorption, Eur. J. Appl. Math. 31 (2020), no. 3, 385–406. [4] L. Alvarez, J.I. Diaz, and R. Kersner, On the initial growth of the interfaces in nonlinear diffusion-convection processes, Nonlinear Diffusion Equations and Their Equilibrium States I, Springer, New York, NY., 1988, pp. 1–20. [5] R.O. Ayeni and F.B. Agusto, On the existence and uniqueness of self-similar diffusion equation, J. Nig. Ass. Math. Phys. 44 (2000), 183. [6] S.N. Antontsev, J.I. Diaz, S. Shmarev, and A.J. Kassab, Energy methods for free boundary problems: Applications to nonlinear PDEs and fluid mechanics, Progress in Nonlinear Differential Equations and Their Applications, 48. Appl. Mech. Rev.,55 (2002), no. 4, B74–B75. [7] L. Boccardo and T. Gallouet, Summability of the solutions of nonlinear elliptic equations with right-hand side measures, J. Convex Anal. 3 (1996), 361–366. [8] L.A. Caffarelli and J.L. Vazquez, Nonlinear porous medium flow with fractional potential pressure, Arch. Ration. Mech. Anal. 202 (2011), no. 2, 537—565. [9] R. Cherniha and M. Serov, Lie and non-lie symmetries of non-linear diffusion equations with convection term, Symm. Non-linear Math. Phys. 2 (1997), 444–449. [10] J.I. Diaz, Nonlinear partial differential equations and free boundaries, Elliptic Equations. Res. Notes Math. 1 (1985), 106. [11] A. de Pablo and A. Sanchez, Global travelling waves in reaction convection-diffusion equations, J. Differ. Equ. 165 (2000), no. 2, 377–413. [12] E. DiBenedetto, Degenerate Parabolic Equations, Springer Verlag, Series University text, New York, 1993. [13] E. DiBenedetto and M.A. Herrero, On the Cauchy problem and initial traces for a degenerate parabolic equation, Trans. Amer. Math. Soc. 314 (1989), no. 1, 187–224. [14] J.R. Esteban and J.L. Vazquez, On the equation of turbulent filtration in one-dimensional porous media, Nonlinear Anal.: Theory Meth. Appl. 10 (1986), no. 11, 1303–1325. [15] F. Ettwein and M. Ruzicka, Existence of strong solutions for electromagnetical fluids in two dimensions: steady Dirichlet problem, Geometric Analysis and Nonlinear Partial Differential Equations, Springer, Berlin, Heidelberg, 2003, pp. 591–602. [16] A.L. Gladkov, The Cauchy problem in classes of increasing functions for the equation of filtration with convection, Sbornik: Math. 186 (1995), no. 6, 803–825. [17] K. Ishige, On the existence of solutions of the Cauchy problem for a doubly nonlinear parabolic equation, SIAM J. Math. Anal. 27 (1996), no. 5, 1235–1260. [18] A.S. Kalashnikov, Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations, Russian Math. Surv. 42 (1987), no. 2, 169–222. [19] R. Kuske and P. Milemski, Modulated two-dimensional patterns in reaction-diffusion systems, Eur. J. Appl. Math. 10 (1999), 157–184. [20] K.I. Nakamura, H. Matano, D. Hilhorst, and R. Schaatzle, Singular limit of a reaction-diffusion equation with a spatially inhomogeneous reaction term, J. Statist. Phys. 95 (1999), 1165–1185. | ||
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