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(1964)
Asymptotics of a Solution of Integro-Differential Equation with a Small Parameter Multiplying the Derivative
E.F. Mishchenko, N.Kh. andRozov (1975)
Differentsial’nye uravneniya s malym parametrom i relaksatsionnye kolebaniya
Daniel Henry (1989)
Geometric Theory of Semilinear Parabolic Equations
(1975)
Differentsial'nye uravneniya s malym parametrom i relaksatsionnye kolebaniya (Differential Equations with Small Parameter and Relaxation Oscillations)
N. Nefedov, A. Nikitin (2006)
Method of differential inequalities for step-like contrast structures in singularly perturbed integro-differential equations in the spatially two-dimensional caseDifferential Equations, 42
A.B. Vasil’eva, V.F. Butuzov (1973)
Asimptoticheskie razlozheniya reshenii singulyarno vozmushchennykh uravnenii
N.N. Nefedov, A.G. Nikitin (2006)
Method of Differential Inequalities for Step-Like Contrast Structures in Singularly Perturbed Integro-Differential Equations in the Spatially Two-Dimensional CaseDiffer. Uravn., 42
(2009)
Geometricheskaya dekompozitsiya singulyarno vozmushchennykh sistem (Geometric Decomposition of Singularly Perturbed Systems
A.N. Filatov, L.V. Sharova (1976)
Integral’nye neravenstva i teoriya nelineinykh kolebanii
A.B. Vasil’eva, V.F. Butuzov (1990)
Asimptoticheskie metody v teorii singulyarnykh vozmushchenii
R. Anderson, R. May (1981)
The Population Dynamics of Microparasites and Their Invertebrate HostsPhilosophical Transactions of the Royal Society B, 291
A. Korobeinikov, Conor Dempsey (2014)
A continuous phenotype space model of RNA virus evolution within a hostMathematical Biosciences and Engineering, 11
R.M. Anderson, R.M. May (1981)
The Population Dynamics of Microparasites and Their Invertebrate HostsPhilos. Trans. R. Soc. Lond. Ser. B 291, 291
S. Wain-Hobson (2001)
Virus Dynamics: Mathematical Principles of Immunology and VirologyNature Medicine, 7
N.N. Nefedov, A.G. Nikitin (2012)
Initial–Boundary Value Problem for Nonlocal Singularly Perturbed Reaction–Diffusion EquationZh. Vychisl. Mat. Mat. Fiz., 52
N.N. Nefedov, A.G. Nikitin (2000)
Method of Differential Inequalities for Singularly Perturbed Integro-Differential EquationsDiffer. Uravn., 36
Gang Huang, Y. Takeuchi, A. Korobeinikov (2012)
HIV evolution and progression of the infection to AIDS.Journal of theoretical biology, 307
N. Nefedov, A. Nikitin (2012)
The initial boundary value problem for a nonlocal singularly perturbed reaction-diffusion equationComputational Mathematics and Mathematical Physics, 52
(1976)
Integral’nye neravenstva i teoriya nelineinykh kolebanii (Integral Inequalities and Theory of Nonlinear Oscillations)
(1981)
Translated under the title Geometricheskaya teoriya polulineinykh parabolicheskikh uravnenii
N.V. Voropaeva, V.A. Sobolev (2009)
Geometricheskaya dekompozitsiya singulyarno vozmushchennykh sistem
(1990)
Asimptoticheskie metody v teorii singulyarnykh vozmushchenii (Asymptotic Methods in Singular Perturbation Theory)
We study an initial–boundary value problem for a singularly perturbed system of partial integro-differential equations. We prove a theorem on the passage to the limit. The result is used to decrease the dimension of a virus evolution model. We construct an asymptotic solution by the Tikhonov–Vasil’eva boundary function method. The analytic results obtained are compared with a numerical study of the system.
Differential Equations – Springer Journals
Published: Oct 19, 2016
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