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| 2. |
- Beilina, Larisa, 1970, et al.
(författare)
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Determining the conductivity for a nonautonomous hyperbolic operator in a cylindrical domain
- 2018
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Ingår i: Mathematical Methods in the Applied Sciences. - : Wiley. - 0170-4214 .- 1099-1476. ; 41:5, s. 2012-2030
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Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted to the reconstruction of the conductivity coefficient for a nonautonomous hyperbolic operator an infinite cylindrical domain. Applying a local Carleman estimate, we prove the uniqueness and a Holder stability in the determination of the conductivity using a single measurement data on the lateral boundary. Our numerical examples show good reconstruction of the location and contrast of the conductivity function in 3 dimensions.
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| 3. |
- Bock, Wolfgang, et al.
(författare)
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On the potential in non-Gaussian chain polymer models
- 2019
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Ingår i: Mathematical methods in the applied sciences. - : John Wiley & Sons. - 0170-4214 .- 1099-1476. ; 42:18, s. 7452-7460
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we investigate the potential for a class of non-Gaussian processes so-called generalized grey Brownian motion. We obtain a closed analytic form for the potential as an integral of the M-Wright functions and the Green function. In particular, we recover the special cases of Brownian motion and fractional Brownian motion. In addition, we give the connection to a fractional partial differential equation and its the fundamental solution.
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| 4. |
- Bock, Wolfgang, et al.
(författare)
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Optimal control and basic reproduction numbers for a compartmental spatial multipatch dengue model
- 2018
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Ingår i: Mathematical methods in the applied sciences. - : Elsevier. - 0170-4214 .- 1099-1476. ; 41:9, s. 3231-3245
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Tidskriftsartikel (refereegranskat)abstract
- Dengue is a vector-borne viral disease increasing dramatically over the past years due to improvement in human mobility. In this work, a multipatch model for dengue transmission dynamics is studied, and by that, the control efforts to minimize the disease spread by host and vector control are investigated. For this model, the basic reproduction number is derived, giving a choice for parameters in the endemic case. The multipatch system models the host movement within the patches, which coupled via a residence-time budgeting matrix P. Numerical results confirm that the control mechanism embedded in incidence rates of the disease transmission effectively reduces the spread of the disease.
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| 5. |
- Buchukuri, Tengiz, et al.
(författare)
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Laplace–Beltrami equation on hypersurfaces and Γ-convergence
- 2017
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Ingår i: Mathematical methods in the applied sciences. - : John Wiley & Sons. - 0170-4214 .- 1099-1476. ; 40:13, s. 4637-4657
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Tidskriftsartikel (refereegranskat)abstract
- A mixed boundary value problem for the stationary heat transfer equation in a thin layer around a surface C with the boundary is investigated. The main objective is to trace what happens in Γ-limit when the thickness of the layer converges to zero. The limit Dirichlet BVP for the Laplace–Beltrami equation on the surface is described explicitly, and we show how the Neumann boundary conditions in the initial BVP transform in the Γ-limit. For this, we apply the variational formulation and the calculus of Günter's tangential differential operators on a hypersurface and layers, which allow global representation of basic differential operators and of corresponding boundary value problems in terms of the standard Euclidean coordinates of the ambient space Rn.
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| 6. |
- Careaga, Julio, et al.
(författare)
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Entropy solutions and flux identification of a scalar conservation law modelling centrifugal sedimentation
- 2020
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Ingår i: Mathematical Methods in the Applied Sciences. - : Wiley. - 0170-4214 .- 1099-1476. ; 43:7, s. 4530-4557
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Tidskriftsartikel (refereegranskat)abstract
- Centrifugal sedimentation of an ideal suspension in a rotating tube or basket can be modelled by an initial-boundary-value problem for a scalar conservation law with a nonconvex flux function. The sought unknown is the volume fraction of solids as function of radial distance and time for constant initial data. The method of characteristics is used to construct entropy solutions. The qualitatively different solutions, which depend on the initial value and the vessel radial coordinates, are presented in detail along with numerical simulations. Based on the entropy solutions, a new method of flux identification, which does not require any prescribed functional expression, is presented and illustrated with synthetic data.
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| 7. |
- Drosinou, Ourania, et al.
(författare)
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A study of a nonlocal problem with Robin boundary conditions arising from technology
- 2021
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Ingår i: Mathematical methods in the applied sciences. - : Wiley-Blackwell. - 0170-4214 .- 1099-1476. ; 44:13, s. 10084-10120
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Tidskriftsartikel (refereegranskat)abstract
- In the current work, we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (micro-electro-mechanical system) device, when the ends of the device are attached or pinned to a cantilever. Initially, the steady-state problem is investigated estimates of the pull-in voltage are derived. In particular, a Pohožaev's type identity is also obtained, which then facilitates the derivation of an estimate of the pull-in voltage for radially symmetric N-dimensional domains. Next a detailed study of the time-dependent problem is delivered and global-in-time as well as quenching results are obtained for generic and radially symmetric domains. The current work closes with a numerical investigation of the presented nonlocal model via an adaptive numerical method. Various numerical experiments are presented, verifying the previously derived analytical results as well as providing new insights on the qualitative behavior of the studied nonlocal model.
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| 8. |
- Eden, Michael, 1987-, et al.
(författare)
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Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium with a priori known phase transformations
- 2017
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Ingår i: Mathematical methods in the applied sciences. - : John Wiley & Sons. - 0170-4214 .- 1099-1476. ; 40:11, s. 3955-3972
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Tidskriftsartikel (refereegranskat)abstract
- We investigate a linear, fully coupled thermoelasticity problem for a highly heterogeneous, two-phase medium. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing an a prioriknown interface movement because of phase transformations. After transforming the moving geometry to an ϵ-periodic, fixed reference domain, we establish the well-posedness of the model and derive a number of ϵ-independent a priori estimates. Via a two-scale convergence argument, we then show that the ϵ-dependent solutions converge to solutions of a corresponding upscaled model with distributed time-dependent microstructures.
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| 9. |
- Eden, Michael, 1987-, et al.
(författare)
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Homogenization of a poroelasticity model for fiber‐reinforced hydrogels
- 2022
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Ingår i: Mathematical methods in the applied sciences. - : John Wiley & Sons. - 0170-4214 .- 1099-1476. ; 45:17, s. 11562-11580
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the analysis and homogenization of a poroelastic model for the hydro-mechanical response of fiber-reinforced hydrogels are considered. Here, the medium in question is considered to be a highly heterogeneous two-component media composed of a connected fiber-scaffold with periodically distributed inclusions of hydrogel. While the fibers are assumed to be elastic, the hydromechanical response of hydrogel is modeled via Biot's poroelasticity.We show that the resulting mathematical problem admits a unique weak solution and investigate the limit behavior (in the sense of two-scale convergence) of the solutions with respect to a scale parameter, epsilon to 0, characterizing the heterogeneity of the medium. While doing , we arrive at an effective model where the micro variations of the pore pressure give rise to a micro stress correction at the macro scale.
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| 10. |
- El Fatini, Mohamed, et al.
(författare)
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The effect of stochasticity with respect to reinfection and nonlinear transition states for some diseases with relapse
- 2020
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Ingår i: Mathematical methods in the applied sciences. - : John Wiley & Sons. - 0170-4214 .- 1099-1476. ; 43:18, s. 10659-10670
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider a stochastic epidemic model with relapse, reinfection, and a general incidence function. Using stochastic tools, we establish a stochastic thresholdRs0and prove the extinction of the disease when its value is equal or less than unity. We also show the persistence in mean of the disease whenRs0>1.Moreover, we prove the existence and uniqueness of a stationary distribution. Finally, numerical simulations are presented to show the effectiveness of theoretical results.
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