Mathematik und Statistikhttp://kops.uni-konstanz.de:80/handle/123456789/82019-12-08T04:05:37Z2019-12-08T04:05:37ZGeneralized thermoelastic plates : frequency analysisFischer, Lisapop260039123456789/478192019-12-05T02:13:53Z2019Generalized thermoelastic plates : frequency analysis
Fischer, Lisa
We analyse coupled systems of thermoelastic type given in a general abstract form. We consider a self-adjoint, non-negative operator A on a Hilbert space such that 0 ∈ σ(A). In applications this setting belongs to problems in the whole space case or in exterior domains. Heat conduction is modelled with Fourier's law of heat conduction. In addition we take into consideration an inertial term. A complete picture of the region of smoothing and also the region of regularity loss for the arising parameters is given.
2019Fischer, Lisa510We analyse coupled systems of thermoelastic type given in a general abstract form. We consider a self-adjoint, non-negative operator A on a Hilbert space such that 0 ∈ σ(A). In applications this setting belongs to problems in the whole space case or in exterior domains. Heat conduction is modelled with Fourier's law of heat conduction. In addition we take into consideration an inertial term. A complete picture of the region of smoothing and also the region of regularity loss for the arising parameters is given.WORKINGPAPERurn:nbn:de:bsz:352-2-zidgghbt0hag2engKonstanzer Schriften in Mathematik3872019-12-04T10:42:58+01:00123456789/392019-12-04T09:42:58ZMathematical modelling and optimal control of typhoid feverAbboubakar, Hamadjampop524550Racke, Reinhardpop03677123456789/477682019-12-03T02:14:14Z2019Mathematical modelling and optimal control of typhoid fever
Abboubakar, Hamadjam; Racke, Reinhard
Typhoid fever is a disease caused by a salmonella bacterium (Salmonella typhi) and transmitted by ingestion of water and/or food contaminated with faeces (stool). In this paper, we derive and analyse a model for the control of typhoid fever which takes into account an imperfect vaccine combined with some other control measures already studied in the literature. We begin by analysing the model without control. We compute the basic reproduction number R_0 and prove the local and global stability of the disease-free equilibrium whenever R_0 is less than one through Lyapunov's theory. When R_0 is greater than one, we prove the local asymptotic stability of the unique endemic equilibrium through the Centre Manifold Theory and we find that the model exhibits a forward bifurcation. Then, we extend the model by reformulating it as an optimal control problem, with the use of three time dependent controls, to assess the impact of vaccination combined with protection/environment sanitation and treatment on the spread of the disease in human population. By using optimal control theory, we establish conditions under which the spread of the disease can be stopped, and we examine the impact of combined control tools on the transmission dynamic of the disease. Pontryagin's maximum principle is used to characterize the optimal control. Numerical simulations and efficiency analysis show that, if we want to reduce significantly the spread of typhoid fever, treatment must be taken into account in all control strategies.
2019Abboubakar, HamadjamRacke, Reinhard510Typhoid fever is a disease caused by a salmonella bacterium (Salmonella typhi) and transmitted by ingestion of water and/or food contaminated with faeces (stool). In this paper, we derive and analyse a model for the control of typhoid fever which takes into account an imperfect vaccine combined with some other control measures already studied in the literature. We begin by analysing the model without control. We compute the basic reproduction number R_0 and prove the local and global stability of the disease-free equilibrium whenever R_0 is less than one through Lyapunov's theory. When R_0 is greater than one, we prove the local asymptotic stability of the unique endemic equilibrium through the Centre Manifold Theory and we find that the model exhibits a forward bifurcation. Then, we extend the model by reformulating it as an optimal control problem, with the use of three time dependent controls, to assess the impact of vaccination combined with protection/environment sanitation and treatment on the spread of the disease in human population. By using optimal control theory, we establish conditions under which the spread of the disease can be stopped, and we examine the impact of combined control tools on the transmission dynamic of the disease. Pontryagin's maximum principle is used to characterize the optimal control. Numerical simulations and efficiency analysis show that, if we want to reduce significantly the spread of typhoid fever, treatment must be taken into account in all control strategies.WORKINGPAPERurn:nbn:de:bsz:352-2-ise8u21e4ib13engKonstanzer Schriften in Mathematik3862019-12-02T13:39:11+01:00123456789/392019-12-02T12:39:11ZPOD-based State-Constrained Economic Model Predictive Control for Convection-Diffusion PhenomenaMechelli, Lucapop508278123456789/475382019-11-20T02:13:58Z2019POD-based State-Constrained Economic Model Predictive Control for Convection-Diffusion Phenomena
Mechelli, Luca
Motivated by an application to energy efficient building, in this thesis optimal control of a linear time-dependent convection-diffusion equation is considered together with bilateral control and state constraints. To obtain regular Lagrange multipliers, two different approaches are investigated. The first one is called virtual control approach and it consists in introducing an artificial control, which allows replacing the pointwise state constraints with mixed constraints. The regularized problem is then solved with the Primal Dual Active Set Strategy (PDASS). The second applied technique is the augmented Lagrangian method: penalization terms dependent on the state constraints are added to the cost functional and many only control constrained problems are iteratively solved applying projected gradient or projected BFGS methods. To speed-up the computational time proper orthogonal decomposition (POD) is considered together with an a-posteriori error analysis, which ensures the quality of the POD approximation. Furthermore, model predictive control (MPC) helps to handle the long-time horizon and the problem parameter changes in an efficient way. At last, numerical simulations show the advantages and disadvantages of these techniques.
2019Mechelli, Luca510Motivated by an application to energy efficient building, in this thesis optimal control of a linear time-dependent convection-diffusion equation is considered together with bilateral control and state constraints. To obtain regular Lagrange multipliers, two different approaches are investigated. The first one is called virtual control approach and it consists in introducing an artificial control, which allows replacing the pointwise state constraints with mixed constraints. The regularized problem is then solved with the Primal Dual Active Set Strategy (PDASS). The second applied technique is the augmented Lagrangian method: penalization terms dependent on the state constraints are added to the cost functional and many only control constrained problems are iteratively solved applying projected gradient or projected BFGS methods. To speed-up the computational time proper orthogonal decomposition (POD) is considered together with an a-posteriori error analysis, which ensures the quality of the POD approximation. Furthermore, model predictive control (MPC) helps to handle the long-time horizon and the problem parameter changes in an efficient way. At last, numerical simulations show the advantages and disadvantages of these techniques.DOCTORAL_THESISurn:nbn:de:bsz:352-2-2zoi8n9sxknm1eng2019-11-19T08:27:18+01:00123456789/392019-11-19T07:27:18ZStochastic integration and differential equations for typical pathsBartl, Danielpop224057Kupper, Michaelpop243845Neufeld, Ariel123456789/475222019-11-19T02:13:52Z2019Stochastic integration and differential equations for typical paths
Bartl, Daniel; Kupper, Michael; Neufeld, Ariel
2019Bartl, DanielKupper, MichaelNeufeld, Ariel510JOURNAL_ARTICLEeng10.1214/19-EJP3431083-648924Electronic Journal of Probability2019-11-18T10:38:00+01:00123456789/39Electronic Journal of Probability ; 24 (2019). - 97. - eISSN 1083-6489true2019-11-18T09:38:00Ztrue