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    Academic Journal

    Contributors: This work was supported by Russian fund of basic researches, project No 16-01-00437., Работа выполнена при финансовой поддержке гранта РФФИ, проект №16-01-00437.

    Source: Modeling and Analysis of Information Systems; Том 25, № 1 (2018); 125-132 ; Моделирование и анализ информационных систем; Том 25, № 1 (2018); 125-132 ; 2313-5417 ; 1818-1015

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    Relation: https://www.mais-journal.ru/jour/article/view/637/496; Нефедов Н.Н., Давыдова М.А., “Периодические контрастные структуры в системах типа реакция-диффузия-адвекция”, Дифференциальные уравнения, 46:9 (2010), 1300– 1312; Васильева А.Б., Давыдова М.А., “О контрастной структуре типа ступеньки для одного класса нелинейных сингулярно возмущенных уравнений второго порядка”, Журнал вычислительной математики и математической физики, 38:6 (1998), 938– 947; Васильева А.Б., “О периодических решениях параболической задачи с малым параметром при производных”, Журнал вычислительной математики и математической физики, 43:7 (2003), 975–986; Nefedov N.N., Nikulin E.I., “Existence and stability of periodic contrast structures in the reaction-advection-diffusion problem”, Russian Journal of Mathematical Physics, 22:2 (2015), 215–226.; Нефедов Н.Н., Никулин Е.И., “Существование и устойчивость периодических контрастных структур в задаче реакция-адвекция-диффузия в случае сбалансированной нелинейности”, Дифференциальные уравнения, 53:4 (2017), 524–537

  2. 2
    Academic Journal

    Source: Modeling and Analysis of Information Systems; Том 23, № 3 (2016); 342-348 ; Моделирование и анализ информационных систем; Том 23, № 3 (2016); 342-348 ; 2313-5417 ; 1818-1015

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    Relation: https://www.mais-journal.ru/jour/article/view/348/334; N. N. Nefedov, L. Recke, K. R. Schnieder, “Existence and asymptotic stability of periodic solutions with an interior layer of reaction-advection-diffusion equations.”, Journal of Mathematical Analysis and Applications, 405 (2013), 90–103.; N. N. Nefedov, M. A. Davydova, “Contrast structures in singularly perturbed quasilinear reaction-diffusion-advection equations.”, Differentsial’nye Uravneniya, 49 (2013), 715– 733.; N.N. Nefedov, L. Recke, K.R. Schneider, “Asymptotic stability via the Krein-Rutman theorem for singularly perturbed parabolic periodic-Dirichlet problems.”, Regular and Chaotic Dynamics, 15 (2010), 382–389.; N.N. Nefedov, “The method of differential inequalities for some classes of nonlinear singularly perturbed problems with internal layers.”, Differ. Uravn., 31 (1995), 1142– 1149.; V.T. Volkov and N.N. Nefedov, “Development of the asymptotic method of differential inequalities for investigation of periodic contrast structures in reacton-diffusion-advection equations.”, Differ. Uravn., 46 (2006), 585–593.; A.B. Vasil’eva and V. F. Butuzov, Asymptotic Expansions of the Solutions of Singularly Perturbed Equations (in Russian), Nauka, Moscow, 1973.; P. Hess, Periodic-Parabolic Boundary Value Problems and Positivity, Pitman Research Notes in Math. Series 247, Longman Scientific&Technical, 1991.; D.H. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Math. J. V. 21, N11, (1972), 979–1001.; P. Fife, M. Tang, “Comparison principles for reaction-diffusion systems: Irregular comparison functions and applications to question of stability and speed propagation of front.”, J. Diff. Equations., 40 (1981), 168–175.; V.T. Volkov and N.N. Nefedov, “O periodicheskikh resheniyakh s pogranichnymi sloyami odnoy singulyarno vozmushchennoy modeli reaktsiya-diffuziya.”, Computational Mathematics and Mathematical Physics, 34 (1994), 1307–1315.; N. N. Nefedov, “Development of the Asymptotic Method of Differential Inequalities for Investigation of Periodic Contrast Structures in Reaction–Diffusion Equations.”, Computational Mathematics and Mathematical Physics, 46 (2006), 614–622.; N. N. Nefedov, “Comparison Principle for Reaction-Diffusion-Advection Problems with Boundary and Internal Layers.”, Lecture Notes in Computer Science, 8236 (2013), 62–72.; N. N. Nefedov, O. E. Omel’chenko, “Periodic Step-Like Contrast Structures for a Singularly Perturbed Parabolic Equation.”, Differ. Uravn., 36 (2000), 209–218.; N. N. Nefedov, “An Asymptotic Method of Differential Inequalities for the Investigation of Periodic Contrast Structures: Existence, Asymptotics, and Stability.”, Differ. Uravn., 36 (2000), 262–269.; A. B. Vasil’eva, V. F. Butuzov, N. N. Nefedov, “Kontrastnye struktury v singulyarno vozmushchennykh zadachakh.”, Fundamental’naya i prikladnaya matematika, 4 (1998), 799–851.; C.V. Pao, Nonlinear parabolic and elliptic equations, Plenum Press, New York and London, 1992.; Amman H. Periodic solutions of semilinear parabolic equations in nonlinear analysis New York: Acad. Press, 1978.

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