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Simulation of Flow in Fractured Poroelastic Media: A Comparison of Different Discretization Approaches Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Asymptotic-Numerical Method for Moving Fronts in Two-Dimensional R-D-A Problems

Authors : Vladimir Volkov, Nikolay Nefedov, Eugene Antipov

Published in: Finite Difference Methods,Theory and Applications

Publisher: Springer International Publishing

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Abstract

A singularly perturbed initial-boundary value problem for a parabolic equation known in applications as the reaction-diffusion equation is considered. An asymptotic expansion of the solution with moving front is constructed. Using the asymptotic method of differential inequalities we prove the existence and estimate the asymptotic expansion for such solutions. The method is based on well-known comparison theorems and formal asymptotics for the construction of upper and lower solutions in singularly perturbed problems with internal and boundary layers.

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previous chapter Modeling of Annual Heat and Moisture Diffusion in a Multilayer Wall
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Literature
1.
Vasilieva, A.B., Butuzov, V.F., Nefedov, N.N.: Contrast structures in singularly perturbed problems. J. Fund. Prikl. Math. 4(3), 799–851 (1998)
2.
Volkov, V.T., Grachev, N.E., Nefedov, N.N., Nikolaev, A.N.: On the formation of sharp transition layers in two-dimensional reaction-diffusion models. J. Comp. Math. Math. Phys. 47(8), 1301–1309 (2007)MathSciNetCrossRef
3.
Butuzov, V.F., Nefedov, N.N., Schneider, K.R.: On generation and propagation of sharp transition layers in parabolic problems. Vestnik MGU 3(1), 9–13 (2005)MathSciNet
4.
Bozhevolnov, Y.V., Nefedov, N.N.: Front motion in parabolic reaction-diffusion problem. J. Comp. Math. Math. Phys. 50(2), 264–273 (2010)MathSciNetCrossRef
5.
Nefedov, N.N.: The method of diff. inequalities for some classes of nonlinear singul. perturbed problems. J. Diff. Uravn. 31(7), 1142–1149 (1995)MathSciNet
6.
Fife, P.C., Hsiao, L.: The generation and propagation of internal layers. Nonlinear Anal. Theory Meth. Appl. 12(1), 19–41 (1998)MathSciNetCrossRef
7.
Volkov, V., Nefedov, N.: Asymptotic-numerical investigation of generation and motion of fronts in phase transition models. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) NAA 2012. LNCS, vol. 8236, pp. 524–531. Springer, Heidelberg (2013) CrossRef
Metadata
Title
Asymptotic-Numerical Method for Moving Fronts in Two-Dimensional R-D-A Problems
Authors
Vladimir Volkov
Nikolay Nefedov
Eugene Antipov
Copyright Year
2015
Book
Finite Difference Methods,Theory and Applications

Print ISBN: 978-3-319-20238-9

Electronic ISBN: 978-3-319-20239-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-20239-6_46

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