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Kozlov, Vladimir, Professor
Alternative names
Publications (10 of 103) Show all publications
Kozlov, V. & Rossmann, J. (2023). On the Neumann problem for the nonstationary Stokes system in angles and cones. Mathematische Nachrichten, 296(4), 1504-1533
Open this publication in new window or tab >>On the Neumann problem for the nonstationary Stokes system in angles and cones
2023 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 296, no 4, p. 1504-1533Article in journal (Refereed) Published
Abstract [en]

The authors consider the Neumann problem for the nonstationary Stokes system in a two-dimensional angle or a three-dimensional cone. They obtain existence and uniqueness results for solutions in weighted Sobolev spaces and prove a regularity assertion for the solutions.

Place, publisher, year, edition, pages
WILEY-V C H VERLAG GMBH, 2023
Keywords
conical points; Neumann boundary conditions; nonstationary Stokes system
National Category
Algebra and Logic
Identifiers
urn:nbn:se:liu:diva-191737 (URN)10.1002/mana.202100115 (DOI)000919108900001 ()
Available from: 2023-02-13 Created: 2023-02-13 Last updated: 2024-02-29Bibliographically approved
Chepkorir, J., Berntsson, F. & Kozlov, V. (2023). Solving stationary inverse heat conduction in a thin plate. Partial Differential Equations and Applications, 4(6)
Open this publication in new window or tab >>Solving stationary inverse heat conduction in a thin plate
2023 (English)In: Partial Differential Equations and Applications, ISSN 2662-2971, Vol. 4, no 6Article in journal (Refereed) Published
Abstract [en]

We consider a steady state heat conduction problem in a thin plate. In the application, it is used to connect two cylindrical containers and fix their relative positions. At the same time it serves to measure the temperature on the inner cylinder. We derive a two dimensional mathematical model, and use it to approximate the heat conduction in the thin plate. Since the plate has sharp edges on the sides the resulting problem is described by a degenerate elliptic equation. To find the temperature in the interior part from the exterior measurements, we formulate the problem as a Cauchy problem for stationary heat equation. We also reformulate the Cauchy problem as an operator equation, with a compact operator, and apply the Landweber iteration method to solve the equation. The case of the degenerate elliptic equation has not been previously studied in this context. For numerical computation, we consider the case where noisy data is present and analyse the convergence.

Keywords
Cauchy problem, Stationary heat equation, Degenerate elliptic equation, Landweber iterative method
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-201113 (URN)10.1007/s42985-023-00267-7 (DOI)
Available from: 2024-02-22 Created: 2024-02-22 Last updated: 2024-02-22Bibliographically approved
Achieng, P., Berntsson, F., Chepkorir, J. & Kozlov, V. (2021). Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations. Bulletin of the Iranian Mathematical Society, 47, 1681-1699
Open this publication in new window or tab >>Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations
2021 (English)In: Bulletin of the Iranian Mathematical Society, ISSN 1735-8515, Vol. 47, p. 1681-1699Article in journal (Refereed) Published
Abstract [en]

The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers k2, in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of k2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.

Place, publisher, year, edition, pages
Springer, 2021
Keywords
Helmholtz equation, Cauchy problem, Inverse problem, Ill-posed problem
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-170834 (URN)10.1007/s41980-020-00466-7 (DOI)000575739300001 ()2-s2.0-85092146699 (Scopus ID)
Available from: 2020-10-26 Created: 2020-10-26 Last updated: 2024-02-22Bibliographically approved
Andersson, J., Ghersheen, S., Kozlov, V., Tkachev, V. & Wennergren, U. (2021). Effect of density dependence on coinfection dynamics. Analysis and Mathematical Physics, 11(4), Article ID 166.
Open this publication in new window or tab >>Effect of density dependence on coinfection dynamics
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2021 (English)In: Analysis and Mathematical Physics, ISSN 1664-2368, E-ISSN 1664-235X, Vol. 11, no 4, article id 166Article in journal (Refereed) Published
Abstract [en]

In this paper we develop a compartmental model of SIR type (the abbreviation refers to the number of Susceptible, Infected and Recovered people) that models the population dynamics of two diseases that can coinfect. We discuss how the underlying dynamics depends on the carrying capacity K: from a simple dynamics to a more complex. This can also help in understanding the appearance of more complicated dynamics, for example, chaos and periodic oscillations, for large values of K. It is also presented that pathogens can invade in population and their invasion depends on the carrying capacity K which shows that the progression of disease in population depends on carrying capacity. More specifically, we establish all possible scenarios (the so-called transition diagrams) describing an evolution of an (always unique) locally stable equilibrium state (with only non-negative compartments) for fixed fundamental parameters (density independent transmission and vital rates) as a function of the carrying capacity K. An important implication of our results is the following important observation. Note that one can regard the value of K as the natural ‘size’ (the capacity) of a habitat. From this point of view, an isolation of individuals (the strategy which showed its efficiency for COVID-19 in various countries) into smaller resp. larger groups can be modelled by smaller resp. bigger values of K. Then we conclude that the infection dynamics becomes more complex for larger groups, as it fairly maybe expected for values of the reproduction number R0≈1. We show even more, that for the values R0>1 there are several (in fact four different) distinguished scenarios where the infection complexity (the number of nonzero infected classes) arises with growing K. Our approach is based on a bifurcation analysis which allows to generalize considerably the previous Lotka-Volterra model considered previously in Ghersheen et al. (Math Meth Appl Sci 42(8), 2019).

Place, publisher, year, edition, pages
Basel, Switzerland: Birkhaeuser Science, 2021
National Category
Immunology Mathematical Analysis Other Mathematics
Identifiers
urn:nbn:se:liu:diva-179468 (URN)10.1007/s13324-021-00570-9 (DOI)000700279100001 ()34566882 (PubMedID)2-s2.0-85115265043 (Scopus ID)
Note

Funding: Swedish Research Council (VR)Swedish Research Council [2017-03837]

Available from: 2021-09-21 Created: 2021-09-21 Last updated: 2022-05-09Bibliographically approved
Andersson, J., Ghersheen, S., Kozlov, V., Tkachev, V. & Wennergren, U. (2021). Effect of density dependence on coinfection dynamics: part 2. Analysis and Mathematical Physics, 11(4), Article ID 169.
Open this publication in new window or tab >>Effect of density dependence on coinfection dynamics: part 2
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2021 (English)In: Analysis and Mathematical Physics, ISSN 1664-2368, E-ISSN 1664-235X, Vol. 11, no 4, article id 169Article in journal (Refereed) Published
Abstract [en]

In this paper we continue the stability analysis of the model for coinfection with density dependent susceptible population introduced in Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We consider the remaining parameter values left out from Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We look for coexistence equilibrium points, their stability and dependence on the carrying capacity K. Two sets of parameter value are determined, each giving rise to different scenarios for the equilibrium branch parametrized by K. In both scenarios the branch includes coexistence points implying that both coinfection and single infection of both diseases can exist together in a stable state. There are no simple explicit expression for these equilibrium points and we will require a more delicate analysis of these points with a new bifurcation technique adapted to such epidemic related problems. The first scenario is described by the branch of stable equilibrium points which includes a continuum of coexistence points starting at a bifurcation equilibrium point with zero single infection strain #1 and finishing at another bifurcation point with zero single infection strain #2. In the second scenario the branch also includes a section of coexistence equilibrium points with the same type of starting point but the branch stays inside the positive cone after this. The coexistence equilibrium points are stable at the start of the section. It stays stable as long as the product of K and the rate γ¯γ¯ of coinfection resulting from two single infections is small but, after this it can reach a Hopf bifurcation and periodic orbits will appear.

Place, publisher, year, edition, pages
Springer Basel AG, 2021
Keywords
Mathematical Physics, Algebra and Number Theory, Analysis
National Category
Mathematical Analysis Immunology
Identifiers
urn:nbn:se:liu:diva-179802 (URN)10.1007/s13324-021-00602-4 (DOI)000702411500001 ()
Note

Funding: Linkoping University

Available from: 2021-10-03 Created: 2021-10-03 Last updated: 2022-05-09Bibliographically approved
Kozlov, V., Radosavljevic, S., Tkachev, V. & Wennergren, U. (2021). Global stability of an age-structured population model on several temporally variable patches. Journal of Mathematical Biology, 83(6-7), Article ID 68.
Open this publication in new window or tab >>Global stability of an age-structured population model on several temporally variable patches
2021 (English)In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 83, no 6-7, article id 68Article in journal (Refereed) Published
Abstract [en]

We consider an age-structured density-dependent population model on several temporally variable patches. There are two key assumptions on which we base model setupand analysis. First, intraspecific competition is limited to competition between individuals of the same age (pure intra-cohort competition) and it affects density-dependentmortality. Second, dispersal between patches ensures that each patch can be reachedfrom every other patch, directly or through several intermediary patches, within individual reproductive age. Using strong monotonicity we prove existence and uniquenessof solution and analyze its large-time behavior in cases of constant, periodically variable and irregularly variable environment. In analogy to the next generation operator,we introduce the net reproductive operator and the basic reproduction number R0 fortime-independent and periodical models and establish the permanence dichotomy:if R0 ≤ 1, extinction on all patches is imminent, and if R0 > 1, permanence on allpatches is guaranteed. We show that a solution for the general time-dependent problemcan be bounded by above and below by solutions to the associated periodic problems. Using two-side estimates, we establish uniform boundedness and uniform persistenceof a solution for the general time-dependent problem and describe its asymptoticbehaviour

Place, publisher, year, edition, pages
Springer Heidelberg, 2021
Keywords
Applied Mathematics, Agricultural and Biological Sciences (miscellaneous), Modelling and Simulation
National Category
Mathematical Analysis Other Biological Topics
Identifiers
urn:nbn:se:liu:diva-181725 (URN)10.1007/s00285-021-01701-3 (DOI)000727357500001 ()34870739 (PubMedID)
Funder
Linköpings universitet
Note

Funding: Linkoping University

Available from: 2021-12-08 Created: 2021-12-08 Last updated: 2022-01-12
Kozlov, V., Nazarov, S. A. & Zavorokhin, G. (2021). Modeling of Fluid Flow in a Flexible Vessel with Elastic Walls. Journal of Mathematical Fluid Mechanics, 23(3), Article ID 79.
Open this publication in new window or tab >>Modeling of Fluid Flow in a Flexible Vessel with Elastic Walls
2021 (English)In: Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, E-ISSN 1422-6952, Vol. 23, no 3, article id 79Article in journal (Refereed) Published
Abstract [en]

We exploit a two-dimensional model (Ghosh et al. in Q J Mech Appl Math 71(3):349-367, 2018; Kozlov and Nazarov in Dokl Phys 56(11):560-566, 2011, J Math Sci 207(2):249-269, 2015) describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic flows in an infinite cylinder with such intricate boundary conditions. The main result is that solutions of this problem do not depend on the period and they are nothing else but the time independent Poiseuille flow. Similar solutions of the Stokes equations for the rigid wall (the no-slip boundary condition) depend on the period and their profile depends on time.

Place, publisher, year, edition, pages
Springer Nature, 2021
Keywords
Blood vessel with elastic walls; Demension reduction procedure; Periodic in time flows; Poiseuille flow
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:liu:diva-179952 (URN)10.1007/s00021-021-00607-w (DOI)000672674500001 ()2-s2.0-85110649867 (Scopus ID)
Note

Funding Agencies: V.Kozlov was supported by the Swedish Research Council (VR), 2017-03837. S.Nazarov is supported by RFBR grant 18-01-00325. This study was supported by Linköping University, and by RFBR grant 16-31-60112.

Available from: 2021-10-07 Created: 2021-10-07 Last updated: 2021-10-27Bibliographically approved
Andersson, J., Kozlov, V., Radosavljevic, S., Tkachev, V. & Wennergren, U. (2019). Density-Dependent Feedback in Age-Structured Populations. Journal of Mathematical Sciences, 242(1), 2-24
Open this publication in new window or tab >>Density-Dependent Feedback in Age-Structured Populations
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2019 (English)In: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 242, no 1, p. 2-24Article in journal (Refereed) Published
Abstract [en]

The population size has far-reaching effects on the fitness of the population, that, in its turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate predictions about the population dynamics and its asymptotic behaviour. In this paper, we develop a rigourous mathematical analysis to study positive and negative effects of increased population density in the classical nonlinear age-structured population model introduced by Gurtin \& MacCamy in the late 1970s. One of our main results expresses the global stability of the system in terms of the newborn function only. We also derive the existence of a threshold population size implying the population extinction, which is well-known in population dynamics as an Allee effect.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2019
Keywords
Age-Structured Populations
National Category
Mathematics Other Biological Topics
Identifiers
urn:nbn:se:liu:diva-157057 (URN)10.1007/s10958-019-04464-x (DOI)
Available from: 2019-05-24 Created: 2019-05-24 Last updated: 2022-05-09Bibliographically approved
Ghersheen, S., Kozlov, V., Tkachev, V. & Wennergren, U. (2019). Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity. Mathematical methods in the applied sciences, 42(17), 5805-5826
Open this publication in new window or tab >>Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity
2019 (English)In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 42, no 17, p. 5805-5826Article in journal (Refereed) Published
Abstract [en]

Multiple viruses are widely studied because of their negative effect on the health of host as well as on whole population. The dynamics of coinfection are important in this case. We formulated an susceptible infected recovered (SIR) model that describes the coinfection of the two viral strains in a single host population with an addition of limited growth of susceptible in terms of carrying capacity. The model describes five classes of a population: susceptible, infected by first virus, infected by second virus, infected by both viruses, and completely immune class. We proved that for any set of parameter values, there exists a globally stable equilibrium point. This guarantees that the disease always persists in the population with a deeper connection between the intensity of infection and carrying capacity of population. Increase in resources in terms of carrying capacity promotes the risk of infection, which may lead to destabilization of the population.

Place, publisher, year, edition, pages
John Wiley & Sons, 2019
Keywords
carrying capacity, coinfection, global stability, linear complementarity problem, SIR model
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-160293 (URN)10.1002/mma.5671 (DOI)000496512900014 ()2-s2.0-85066086382 (Scopus ID)
Available from: 2019-09-17 Created: 2019-09-17 Last updated: 2020-01-02Bibliographically approved
Kozlov, V., Tkachev, V., Vakulenko, S. & Wennergren, U. (2019). Global stability and persistence of complex foodwebs. Annali di Matematica Pura ed Applicata, 198(5), 1693-1709
Open this publication in new window or tab >>Global stability and persistence of complex foodwebs
2019 (English)In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 198, no 5, p. 1693-1709Article in journal (Refereed) Published
Abstract [en]

We develop a novel approach to study the global behaviour of large foodwebs for ecosystems where several species share multiple resources. The model extends and generalizes some previous works and takes into account self-limitation. Under certain explicit conditions, we establish the global convergence and persistence of solutions.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Global stability, Persistence, Period-two-points, Non-increasing maps, Complex foodwebs, Self-limitation, Multiple resources
National Category
Mathematical Analysis Other Biological Topics
Identifiers
urn:nbn:se:liu:diva-155083 (URN)10.1007/s10231-019-00840-1 (DOI)000492034000012 ()
Available from: 2019-03-15 Created: 2019-03-15 Last updated: 2019-11-11Bibliographically approved
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