Singularly perturbed second order semilinear boundary value problems with interface conditions

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• 作者：Hongxu Lin (1)
  Feng Xie (1)
  
  1. Department of Applied Mathematics ; Donghua University ; Shanghai ; 201620 ; P.R. China
  
• 关键词：34E15 ; 34A36 ; 34B15 ; singular perturbation ; interface conditions ; lower and upper solutions ; asymptotic estimates
• 刊名：Boundary Value Problems
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,049 KB
• 参考文献：1. Mikhailov, M, 脰zisik, M (1994) Unified Analysis and Solutions of Heat and Mass Diffusion. Dover, New York
  2. Falco, C, O鈥橰iordan, E (2010) Interior layers in a reaction-diffusion equation with a discontinuous diffusion coefficient. Int. J. Numer. Anal. Model. 7: pp. 444-461
  3. Chen, CK (2006) A fixed interface boundary value problem for differential equations: a problem arising from population genetics. Dyn. Partial Differ. Equ. 3: pp. 199-208 CrossRef
  4. Aitbayev, R (2013) Existence and uniqueness for a two-point interface boundary value problem. Electron. J. Differ. Equ. 2013: CrossRef
  5. Farrell, PA, Hegarty, AF, Miller, JJH, O鈥橰iordan, E, Shishkin, GI (2004) Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient. Math. Comput. Model. 40: pp. 1375-1392 CrossRef
  6. Farrell, PA, O鈥橰iordan, E, Shishkin, GI (2009) A class of singularly perturbed quasilinear differential equations with interior layers. Math. Comput. 78: pp. 103-127 CrossRef
  7. Huang, Z (2009) Tailored finite point method for the interface problem. Netw. Heterog. Media 4: pp. 91-106 CrossRef
  8. Loubenets, A, Ali, T, Hanke, M (2009) Highly accurate finite element method for one-dimensional elliptic interface problems. Appl. Numer. Math. 59: pp. 119-134 CrossRef
  9. Coster, CD, Habets, P (2006) Two-Point Boundary Value Problems: Lower and Upper Solutions. Elsevier, New York
  10. Vasil茅va, AB, Butuzov, VF, Kalachev, LV (1995) The Boundary Function Method for Singular Perturbation Problems. SIAM, Philadelphia CrossRef
  11. Jager, EM, Jiang, F (1996) The Theory of Singular Perturbations. North-Holland, Amsterdam
  12. Zeidler, E (1995) Applied Functional Analysis: Applications to Mathematical Physics. Springer, New York
  13. Xie, F (2012) On a class of singular boundary value problems with singular perturbation. J. Differ. Equ. 252: pp. 2370-2387 CrossRef
  
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

In this paper we study a class of singularly perturbed interface boundary value problems with discontinuous source terms. We first establish a lemma of lower-upper solutions by using the Schauder fixed point theorem. By the method of boundary functions and the lemma of lower-upper solutions we obtain the existence, asymptotic estimates, and uniqueness of the solution with boundary and interior layers for the proposed problem.