Mathematik und Statistikhttps://kops.uni-konstanz.de:443/handle/123456789/82019-03-20T22:27:39Z2019-03-20T22:27:39ZGlobal well-posedness of the Cauchy problem for the Jordan-Moore-Gibson-Thompson equationRacke, Reinhardpop03677Said-Houari, Belkacempop221203123456789/454792019-03-16T02:14:30Z2019Global well-posedness of the Cauchy problem for the Jordan-Moore-Gibson-Thompson equation
Racke, Reinhard; Said-Houari, Belkacem
In this paper, we consider the Cauchy problem of a third order in time nonlinear equation known as the Jordan-Moore-Gibson-Thompson equation arising in acoustics as an alternative model to the well-known Kuznetsov equation. First, using the contraction mapping theorem, we show a local existence result in appropriate function spaces. Second, by using the energy method together with a bootstrap argument, we prove a global existence result for small data. Third, polynomial decay rates in time for the solution will be obtained for space dimensions N >=2.
2019Racke, ReinhardSaid-Houari, Belkacem510In this paper, we consider the Cauchy problem of a third order in time nonlinear equation known as the Jordan-Moore-Gibson-Thompson equation arising in acoustics as an alternative model to the well-known Kuznetsov equation. First, using the contraction mapping theorem, we show a local existence result in appropriate function spaces. Second, by using the energy method together with a bootstrap argument, we prove a global existence result for small data. Third, polynomial decay rates in time for the solution will be obtained for space dimensions N >=2.WORKINGPAPERurn:nbn:de:bsz:352-2-8ztzhsco3jj82engKonstanzer Schriften in Mathematik3822019-03-15T09:56:19+01:00123456789/392019-03-15T08:56:19ZExponential utility maximization under model uncertainty for unbounded endowmentsBartl, Danielpop224057123456789/454732019-03-15T02:14:47Z2019-02Exponential utility maximization under model uncertainty for unbounded endowments
Bartl, Daniel
We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by dynamically investing in a financial market, and statically in available options.<br /><br />We show that, for any measurable random endowment (regardless of whether the problem is finite or not) an optimal strategy exists, a dual representation in terms of (calibrated) martingale measures holds true, and that the problem satisfies the dynamic programming principle (in case of no options). Further, it is shown that the value of the utility maximization problem converges to the robust superhedging price as the risk aversion parameter gets large, and examples of nondominated probabilistic models are discussed.
2019-02Bartl, Daniel510We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by dynamically investing in a financial market, and statically in available options.<br /><br />We show that, for any measurable random endowment (regardless of whether the problem is finite or not) an optimal strategy exists, a dual representation in terms of (calibrated) martingale measures holds true, and that the problem satisfies the dynamic programming principle (in case of no options). Further, it is shown that the value of the utility maximization problem converges to the robust superhedging price as the risk aversion parameter gets large, and examples of nondominated probabilistic models are discussed.JOURNAL_ARTICLEeng10.1214/18-AAP14281050-51642168-8737577612291The Annals of Applied Probability2019-03-14T14:27:28+01:00123456789/39The Annals of Applied Probability ; 29 (2019), 1. - S. 577-612. - ISSN 1050-5164. - eISSN 2168-8737true2019-03-14T13:27:28ZOn the spectral properties of nonsingular matrices that are strictly sign-regular for some order with applications to totally positive discrete-time systemsAlseidi, Rolapop513822Margaliot, MichaelGarloff, Jürgenpop45676123456789/454542019-03-14T02:14:41Z2019-06On the spectral properties of nonsingular matrices that are strictly sign-regular for some order with applications to totally positive discrete-time systems
Alseidi, Rola; Margaliot, Michael; Garloff, Jürgen
2019-06Alseidi, RolaMargaliot, MichaelGarloff, Jürgen510JOURNAL_ARTICLEeng10.1016/j.jmaa.2019.01.0620022-247X1096-08135245434741Journal of Mathematical Analysis and Applications2019-03-13T14:55:47+01:00123456789/39Journal of Mathematical Analysis and Applications ; 474 (2019), 1. - S. 524-543. - ISSN 0022-247X. - eISSN 1096-0813true2019-03-13T13:55:47ZtrueThe Cauchy problem for thermoelastic plates with two temperaturesRacke, Reinhardpop03677Ueda, Yoshihiropop507668123456789/454032019-03-12T02:14:51Z2019The Cauchy problem for thermoelastic plates with two temperatures
Racke, Reinhard; Ueda, Yoshihiro
We consider the decay rates of solutions to thermoelastic systems in materials where, in contrast to classical thermoelastic models for Kirchhoff type plates, two temperatures are involved, related by an elliptic equation. The arising initial value problems deal with systems of partial differential equations involving Schrödinger like equations, hyperbolic and elliptic equations. Depending on the model -- with Fourier or with Cattaneo type heat conduction -- we obtain polynomial decay rates without or with regularity loss. This way we obtain another example where the loss of regularity in the Cauchy problem corresponds to the loss of exponential stability in bounded domains. The well-posedness is done using semigroup theory in appropriate space reflecting the different regularity compared to the classical single temperature case, and the (optimal) decay estimates are obtained with sophisticated pointwise estimates in Fourier space.
2019Racke, ReinhardUeda, Yoshihiro510We consider the decay rates of solutions to thermoelastic systems in materials where, in contrast to classical thermoelastic models for Kirchhoff type plates, two temperatures are involved, related by an elliptic equation. The arising initial value problems deal with systems of partial differential equations involving Schrödinger like equations, hyperbolic and elliptic equations. Depending on the model -- with Fourier or with Cattaneo type heat conduction -- we obtain polynomial decay rates without or with regularity loss. This way we obtain another example where the loss of regularity in the Cauchy problem corresponds to the loss of exponential stability in bounded domains. The well-posedness is done using semigroup theory in appropriate space reflecting the different regularity compared to the classical single temperature case, and the (optimal) decay estimates are obtained with sophisticated pointwise estimates in Fourier space.WORKINGPAPERurn:nbn:de:bsz:352-2-1uoi41ru65b061engKonstanzer Schriften in Mathematik3812019-03-11T10:44:40+01:00123456789/392019-03-11T09:44:40Z