حول الحلول المنفجرة لنظام من نوع القطع المكافئ مقترن في كل من المعادلات والشروط الحدودية
محتوى المقالة الرئيسي
الملخص
يهتم هذا البحث بالحلول المنفجرة لنظام يتكون من معادلتي انتشارو رد الفعل مقترنتين في كلا من المعادلات والشروط الحدودية. لغرض فهم كيفية تاثير مقاطع رد العفل والشروط الحدودية على خواص الانفجار، تم القيام باشتقاق القيد السفلي والعلوي للانفجار. علاوة على ذلك، تمت دراسة مجموعة النقاط المنفجرة تحت شروط محددة.
Received 6/9/2019, Accepted 20/5/2020, Published Online First 11/1/2021
تفاصيل المقالة
هذا العمل مرخص بموجب Creative Commons Attribution 4.0 International License.
كيفية الاقتباس
المراجع
Rasheed M A. On Blow-up Solutions of Parabolic Problems, Ph.D. thesis, School of physical and Mathematical sciences, University of Sussex, UK; 2012.
Liu W, Zhuang H. Global existence, asymptotic behavior and blow-up of solutions for a suspension bridge equation with nonlinear damping and source terms. Nonlinear Differ. Equ. Appl. 2017; 24(6): doi.org/10.1007/s00030-017-0491-5
Rasheed M A , Al-Dujaly H A S, Aldhlki T J. Blow-Up Rate Estimates for a System of Reaction-Diffusion Equations with Gradient Terms. Int. J. Math. Math. Sci. 2019; 2019(1); 1-7.
Han Y. Blow-up at infinity of solutions to a semilinear heat equation with logarithmic nonlinearity. J. Math. Anal. Appl. 2019; 474(1): 513–517.
Cho CH. A numerical algorithm for blow-up problems revisited. NUMER ALGORITHMS. 2017 Jul 1;75(3):675-97.
Polyanin A D, Shingareva I K. Nonlinear problems with blow-up solutions: Numerical integration based on differential and nonlocal transformations, and differential constraints. Appl Math Comput. 2018; 336: 107–137.
Polyanin A D , Shingareva I K. Nonlinear blow-up problems for systems of ODEs and PDEs: Non-local transformations, numerical and exact solutions. Int J Nonlin Mech. 2019; 111: 28–41.
Fu SC , Guo J S. Blow-up for a semilinear reaction-diffusion system coupled in both equations and boundary conditions. J. Math. Anal. Appl. 2002; 29: 458- 475.
Zheng S N, Li F J. Critical exponent for a reaction-diffusion model with absorption and coupled boundary flux. Proc. Edinb. Math. Soc. 2005; 48: 241-252.
Xu S. Non-simultaneous blow-up of a reaction-diffusion system with inner absorption and coupled via nonlinear boundary flux. Bound Value Probl. 2015; 2015(1). doi:10.1186/s13661-015-0483-5
Ding J, & Hu H. Blow-up solutions for nonlinear reaction diffusion equations under Neumann boundary conditions. Appl Anal. 2016; 96(4): 549-562.
Gladkov A. Blow-up problem for semilinear heat equation with nonlinear nonlocal Neumann boundary condition. Commun Pur Appl Anal. 2017; 16(6): 2053–2068.
Liu B, Dong M., Li F. Asymptotic properties of blow-up solutions in reaction–diffusion equations with nonlocal boundary flux. Z. Angew. Math. Phys. 2018; 69(2): doi:10.1007/s00033-018-0920-2.
Lin Z, Xie C. The blow-up rate for a system of heat equations with Neumann boundary conditions. Acta Math. Sinica. 1999; 15: 549-554.
Deng K. Blow-up rates for parabolic systems, Z. Angew. Math. Phys. 1996; 47:132-143.
Ladyzenskaja OA, Solonnikov VA,Uralceva NN. Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs. JAMS. 23, 1968.
Pao C V. Nonlinear Parabolic and Elliptic Equations. New York and London: Plenum Press, 1992.
Hu B, Yin HM. The profile near blow-up time for solution of the heat equation with a non-linear boundary condition. Trans. Amer. Math. Soc. 1994; 346: 117-135.
Friedman A. Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964.
Quittner P, Souplet Ph. Superlinear Parabolic Problems. Blow-up, Global Existence and Steady States, Birkhuser Advanced Texts, Birkhuser, Basel. 2007.