Existence, uniqueness and continuous dependence on the parameter of solutions of a system of differential equations with deviating argument
S. Czerwik (1977)
Annales Polonici Mathematici
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S. Czerwik (1977)
Annales Polonici Mathematici
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Winkler, Jörg (1993)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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P. Besala (1983)
Annales Polonici Mathematici
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T. Śliwa (1988)
Applicationes Mathematicae
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Qianqian Hou, Xiaojing Xu (2014)
Colloquium Mathematicae
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We prove that strong solutions of the Boussinesq equations in 2D and 3D can be extended as analytic functions of complex time. As a consequence we obtain the backward uniqueness of solutions.
C. Olech, A. Pliś (1967)
Colloquium Mathematicae
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Josef Malík (2004)
Applications of Mathematics
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A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic...
Ralph de Laubenfels (1988)
Studia Mathematica
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Eric Nabana (1999)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Rebelo, C. (2000)
Portugaliae Mathematica
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Dalibor Pražák, Kumbakonam R. Rajagopal (2016)
Commentationes Mathematicae Universitatis Carolinae
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We study the vibrations of lumped parameter systems, the spring being defined by the classical linear constitutive relationship between the spring force and the elongation while the dashpot is described by a general implicit relationship between the damping force and the velocity. We prove global existence of solutions for the governing equations, and discuss conditions that the implicit relation satisfies that are sufficient for the uniqueness of solutions. We also present some counterexamples...
Krzysztof A. Topolski (2015)
Annales Polonici Mathematici
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We present an existence theorem for the Cauchy problem related to linear partial differential-functional equations of an arbitrary order. The equations considered include the cases of retarded and deviated arguments at the derivatives of the unknown function. In the proof we use Tonelli's constructive method. We also give uniqueness criteria valid in a wide class of admissible functions. We present a set of examples to illustrate the theory.
Luis Vega, Nicola Visciglia (2008)
Bollettino dell'Unione Matematica Italiana
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We extend in a nonlinear context previous results obtained in [8], [9], [10]. In particular we present a precised version of Morawetz type estimates and a uniqueness criterion for solutions to subcritical NLS.