This article is cited in 8 scientific papers (total in 8 papers)
On the Solvability of Boundary Value Problems for the Quasilinear Ultraparabolic Equations of Certain Mathematical Models of the Dynamics of Biological Systems
Abstract:
We consider the problem of modeling population dynamics. Mathematically this problem reduces to studying the solvability of a nonlocal boundary value problem for a quasilinear ultraparabolic equation with astronomic time t and biological time a (the age). In the problem under study we prove the existence and uniqueness theorem for regular solutions.
Keywords:
population dynamics, nonlinear ultraparabolic equation, nonlocal boundary value problem, existence of solutions, properties of solutions.
Citation:
A. I. Kozhanov, “On the Solvability of Boundary Value Problems for the Quasilinear Ultraparabolic Equations of Certain Mathematical Models of the Dynamics of Biological Systems”, Sib. Zh. Ind. Mat., 12:4 (2009), 64–78; J. Appl. Industr. Math., 4:4 (2010), 512–525
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\by A.~I.~Kozhanov
\paper On the Solvability of Boundary Value Problems for the Quasilinear Ultraparabolic Equations of Certain Mathematical Models of the Dynamics of Biological Systems
\jour Sib. Zh. Ind. Mat.
\yr 2009
\vol 12
\issue 4
\pages 64--78
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2668812}
\transl
\jour J. Appl. Industr. Math.
\yr 2010
\vol 4
\issue 4
\pages 512--525
\crossref{https://doi.org/10.1134/S199047891004006X}
Linking options:
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https://www.mathnet.ru/eng/sjim/v12/i4/p64
This publication is cited in the following 8 articles:
Kuznetsov I., Sazhenkov S., “Singular Limits of the Quasi-Linear Kolmogorov-Type Equation With a Source Term”, J. Hyberbolic Differ. Equ., 18:04 (2021), 789–856
Jleli M., Samet B., Zhou Y., “On Fujita Critical Exponent For a Nonlinear Ultraparabolic Equation in An Exterior Domain”, J. Math. Anal. Appl., 477:1 (2019), 476–487
Avalishvili G., Avalishvili M., “Nonclassical Problem For Ultraparabolic Equation in Abstract Spaces”, J. Funct. space, 2016, 5687920
Vo Anh Khoa, Tuan Nguyen Huy, Le Trong Lan, Nguyen Thi Yen Ngoc, “A Finite Difference Scheme For Nonlinear Ultra-Parabolic Equations”, Appl. Math. Lett., 46 (2015), 70–76
Lyubanova A.Sh., “On Nonlocal Problems For Systems of Parabolic Equations”, J. Math. Anal. Appl., 421:2 (2015), 1767–1778
Nguyen Huy Tuan, Vo Anh Khoa, Le Trong Lan, Tran The Hung, “On the Regularization of Solution of An Inverse Ultraparabolic Equation Associated With Perturbed Final Data”, J. Inequal. Appl., 2015, 13
G. A. Sviridyuk, S. A. Zagrebina, “Neklassicheskie modeli matematicheskoi fiziki”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 14, 7–18
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