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Kozlov, Vladimir
Alternative names
Publications (10 of 87) Show all publications
Berntsson, F., Karlsson, M., Kozlov, V. & Nazarov, S. A. (2016). A one-dimensional model of viscous blood flow in an elastic vessel. Applied Mathematics and Computation, 274, 125-132
Open this publication in new window or tab >>A one-dimensional model of viscous blood flow in an elastic vessel
2016 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 274, p. 125-132Article in journal (Refereed) Published
Abstract [en]

In this paper we present a one-dimensional model of blood flow in a vessel segment with an elastic wall consisting of several anisotropic layers. The model involves two variables: the radial displacement of the vessels wall and the pressure, and consists of two coupled equations of parabolic and hyperbolic type. Numerical simulations on a straight segment of a blood vessel demonstrate that the model can produce realistic flow fields that may appear under normal conditions in healthy blood vessels; as well as flow that could appear during abnormal conditions. In particular we show that weakening of the elastic properties of the wall may provoke a reverse blood flow in the vessel. (C) 2015 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE INC, 2016
Keyword
Blood flow; Linear model; Asymptotic analysis; Dimension reduction; Numerical simulation
National Category
Mathematics Mechanical Engineering
Identifiers
urn:nbn:se:liu:diva-124453 (URN)10.1016/j.amc.2015.10.077 (DOI)000367521900013 ()
Available from: 2016-02-02 Created: 2016-02-01 Last updated: 2017-11-30
Kozlov, V. A. & Nazarov, S. A. (2016). A simple one-dimensional model of a false aneurysm in the femoral artery. Journal of Mathematical Sciences, 214(3), 287-301
Open this publication in new window or tab >>A simple one-dimensional model of a false aneurysm in the femoral artery
2016 (English)In: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 214, no 3, p. 287-301Article in journal (Refereed) Published
Abstract [en]

Using the dimension reduction procedure, a one-dimensional model of a periodic blood flow in the artery through a small hole in a thin elastic wall to a spindle-shaped hematoma, is constructed. This model is described by a system of two parabolic and one hyperbolic equations provided with mixed boundary and periodicity conditions. The blood exchange between the artery and the hematoma is expressed by the Kirchhoff transmission conditions. Despite the simplicity, the constructed model allows us to describe the damping of a pulsating blood flow by the hematoma and to determine the condition of its growth. In medicine, the biological object considered is called a false aneurysm.

Place, publisher, year, edition, pages
Springer, 2016
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-127727 (URN)10.1007/s10958-016-2778-1 (DOI)
Available from: 2016-05-11 Created: 2016-05-11 Last updated: 2017-11-30Bibliographically approved
Kozlov, V. & Thim, J. (2016). Hadamard type asymptotics for eigenvalues of the Neumann problem for elliptic operators. Journal of Spectral Theory, 6(1), 99-135
Open this publication in new window or tab >>Hadamard type asymptotics for eigenvalues of the Neumann problem for elliptic operators
2016 (English)In: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403, Vol. 6, no 1, p. 99-135Article in journal (Refereed) Published
Abstract [en]

This paper considers how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain. The proximity of two domains is measured in terms of the norm of the difference between the two resolvents corresponding to the reference domain and the perturbed domain, and the size of eigenfunctions outside the intersection of the two domains. This construction enables the possibility of comparing both nonsmooth domains and domains with different topology. An abstract framework is presented, where the main result is an asymptotic formula where the remainder is expressed in terms of the proximity quantity described above when this is relatively small. As an application, we develop a theory for the Laplacian in Lipschitz domains. In particular, if the domains are assumed to be C-1,C-alpha regular, an asymptotic result for the eigenvalues is given together with estimates for the remainder, and we also provide an example which demonstrates the sharpness of our obtained result.

Place, publisher, year, edition, pages
EUROPEAN MATHEMATICAL SOC, 2016
Keyword
Hadamard formula; domain variation; asymptotics of eigenvalues; Neumann problem
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-129508 (URN)10.4171/JST/120 (DOI)000376418300005 ()
Available from: 2016-06-20 Created: 2016-06-20 Last updated: 2017-11-28
Kozlov, V., Vakulenko, S. & Wennergren, U. (2016). Hamiltonian dynamics for complex food webs. PHYSICAL REVIEW E, 93(3), 032413
Open this publication in new window or tab >>Hamiltonian dynamics for complex food webs
2016 (English)In: PHYSICAL REVIEW E, ISSN 1539-3755, Vol. 93, no 3, p. 032413-Article in journal (Refereed) Published
Abstract [en]

We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2016
National Category
Mathematics Biological Sciences
Identifiers
urn:nbn:se:liu:diva-127435 (URN)10.1103/PhysRevE.93.032413 (DOI)000372724300008 ()27078396 (PubMedID)
Note

Funding Agencies|Linkoping University, Government of Russian Federation [074-U01]; Russian Fund of Basic Research [16-01-00648]; US National Institutes of Health [RO1 OD010936]

Available from: 2016-05-01 Created: 2016-04-26 Last updated: 2016-05-17
Kozlov, V. & Nazarov, A. (2016). Oblique derivative problem for non-divergence parabolic equations with time-discontinuous coefficients in a wedge. Journal of Mathematical Analysis and Applications, 435(1), 210-228
Open this publication in new window or tab >>Oblique derivative problem for non-divergence parabolic equations with time-discontinuous coefficients in a wedge
2016 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 435, no 1, p. 210-228Article in journal (Refereed) Published
Abstract [en]

We consider an oblique derivative problem in a wedge for non-divergence parabolic equations with time-discontinuous coefficients. We obtain weighted coercive estimates of solutions in anisotropic Sobolev spaces. (C) 2015 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE, 2016
Keyword
Parabolic equations in a wedge; Discontinuous coefficients; Weighted coercive estimates; Anisotropic Sobolev spaces
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-124076 (URN)10.1016/j.jmaa.2015.10.029 (DOI)000365928200011 ()
Available from: 2016-01-25 Created: 2016-01-19 Last updated: 2017-11-30
Kozlov, V. & Rossmann, J. (2016). On the nonstationary Stokes system in a cone. Journal of Differential Equations, 260(12), 8277-8315
Open this publication in new window or tab >>On the nonstationary Stokes system in a cone
2016 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 260, no 12, p. 8277-8315Article in journal (Refereed) Published
Abstract [en]

The authors consider the Dirichlet problem for the nonstationary Stokes system in a threedimensional cone. They obtain existence and uniqueness results for solutions in weighted Sobolev spaces and prove a regularity assertion for the solutions. (C) 2016 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE, 2016
Keyword
Nonstationary Stokes system; Conical points
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-128716 (URN)10.1016/j.jde.2016.02.024 (DOI)000375234300001 ()
Available from: 2016-06-07 Created: 2016-05-30 Last updated: 2017-11-30
Kozlov, V., Radosavljevic, S., Tkachev, V. & Wennergren, U. (2016). Persistence analysis of the age-structured population model on several patches. In: J. Vigo-Aguiar (Ed.), Proceedings of the 16th International Conference on Mathematical Methods in Science and Engineering, July 4-8, Rota, Cadiz, Spain, Vol. III: . Paper presented at Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2016 (pp. 717-727). Paper presented at Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2016. Universidad de Cádiz, 3
Open this publication in new window or tab >>Persistence analysis of the age-structured population model on several patches
2016 (English)In: Proceedings of the 16th International Conference on Mathematical Methods in Science and Engineering, July 4-8, Rota, Cadiz, Spain, Vol. III / [ed] J. Vigo-Aguiar, Universidad de Cádiz , 2016, Vol. 3, p. 717-727Chapter in book (Refereed)
Abstract [en]

We consider a system of nonlinear partial differential equations that describes an age-structured population living in changing environment on $N$ patches. We prove existence and uniqueness of solution and analyze large time behavior of the system in time-independent case and for periodically changing environment. Under the assumption that every patch can be reached from every other patch, directly or through several intermediary patches, and that net reproductive operator has spectral radius larger than one, we prove that population is persistent on all patches. If the spectral radius is less or equal one, extinction on all patches is imminent.

Place, publisher, year, edition, pages
Universidad de Cádiz, 2016
Keyword
age-structure, persistence, Kermack-McKendrick equation, Lotcka-Volterra equation
National Category
Biological Sciences Mathematics
Identifiers
urn:nbn:se:liu:diva-130231 (URN)9788460860822 (ISBN)
Conference
Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2016
Note

Associate Editors

P. Schwerdtfeger (New Zealand), W. Sprößig (Germany), N. Stollenwerk (Portugal), Pino Caballero (Spain), J. Cioslowski (Poland), J. Medina (Spain), I. P. Hamilton (Canada), J. A. Alvarez-Bermejo (Spain)

Available from: 2016-07-21 Created: 2016-07-21 Last updated: 2016-08-31Bibliographically approved
Kozlov, V., Nazarov, S. A. & Orlof, A. (2016). Trapped modes supported by localized potentials in the zigzag graphene ribbon. Comptes rendus. Mathematique, 354(1), 63-67
Open this publication in new window or tab >>Trapped modes supported by localized potentials in the zigzag graphene ribbon
2016 (English)In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 354, no 1, p. 63-67Article in journal (Refereed) Published
Abstract [en]

Localized potentials in the Dirac equation for the electron dynamics in a zigzag graphene ribbon are constructed to support trapped modes while the corresponding eigenvalues are embedded into the continuous spectrum. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Place, publisher, year, edition, pages
Elsevier, 2016
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-127590 (URN)10.1016/j.crma.2015.10.007 (DOI)000373518100011 ()
Note

Funding Agencies|Linkoping University; Russian Foundation of Basic Research [15-01-02175]

Available from: 2016-05-03 Created: 2016-05-03 Last updated: 2018-03-06
Kozlov, V. & Nazarov, S. (2015). Asymptotic Models of Anisotropic Heterogeneous Elastic Walls of Blood Vessels. Linköping University Electronic Press
Open this publication in new window or tab >>Asymptotic Models of Anisotropic Heterogeneous Elastic Walls of Blood Vessels
2015 (English)Report (Other academic)
Abstract [en]

Using the dimension reduction procedure in the three-dimensional elasticity system, we derive a two-dimensional model for elastic laminate walls of a blood vessel. The wall of arbitrary cross-section consists of several (actually three) elastic, anisotropic layers. Assuming that the wall’s thickness is small compared with the vessel’s diameter and length, we derive a system of the limit equations. In these equations, the wall’s displacements are unknown given on the two-dimensional boundary of a cylinder, whereas the equations themselves constitute a second order hyperbolic system. This system is coupled with the Navier–Stokes equations through the stress and velocity, i.e. dynamic and kinematic conditions at the interior surface of the wall. Explicit formulas are deduced for the effective rigidity tensor of the wall in two natural cases. The first of them concerns the homogeneous anisotropic laminate layer of constant thickness like that in the wall of a peripheral vein, whereas the second case is related to enforcing of the media and adventitia layers of the artery wall by bundles of collagen fibers. It is also shown that if the blood flow stays laminar, then the describing cross-section of the orthotropic homogeneous blood vessel becomes circular.

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2015. p. 32
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2015:14
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-122467 (URN)LiTH-MAT-R--2015/14--SE (ISRN)
Available from: 2015-11-03 Created: 2015-11-03 Last updated: 2015-11-03
Kozlov, V. & Rossmann, J. (2015). ESTIMATES OF GREENS FUNCTION FOR SECOND-ORDER PARABOLIC EQUATIONS NEAR EDGES. Mathematika, 61(2), 345-369
Open this publication in new window or tab >>ESTIMATES OF GREENS FUNCTION FOR SECOND-ORDER PARABOLIC EQUATIONS NEAR EDGES
2015 (English)In: Mathematika, ISSN 0025-5793, E-ISSN 2041-7942, Vol. 61, no 2, p. 345-369Article in journal (Refereed) Published
Abstract [en]

We consider the first boundary value problem for a second-order parabolic equation with variable coefficients in the domain K x Rn-m, where K is an m-dimensional cone. The main results of the paper are pointwise estimates of the Greens function.

Place, publisher, year, edition, pages
University College London, Faculty of Mathematical and Physical Sciences, Department of Mathematics, 2015
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-118867 (URN)10.1112/S0025579315000091 (DOI)000354285800006 ()
Available from: 2015-06-05 Created: 2015-06-04 Last updated: 2017-12-04
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