Results 11 to 20 of about 38,842 (262)
Operator Ordering and Solution of Pseudo-Evolutionary Equations [PDF]
Axioms, 2019 The solution of pseudo initial value differential equations, either ordinary or partial (including those of fractional nature), requires the development of adequate analytical methods, complementing those well established in the ordinary differential ...
Nicolas Behr +2 more
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Examples of Evolutionary Equations [PDF]
, 2021 AbstractThis chapter is devoted to a small tour through a variety of evolutionary equations. More precisely, we shall look into the equations of poro-elastic media, (time-)fractional elasticity, thermodynamic media with delay as well as visco-elastic media. The discussion of these examples will be similar to that of the examples in the previous chapter
Christian Seifert +2 more
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Semigroups and evolutionary equations [PDF]
Semigroup Forum, 2021 AbstractWe show how strongly continuous semigroups can be associated with evolutionary equations. For doing so, we need to define the space of admissible history functions and initial states. Moreover, the initial value problem has to be formulated within the framework of evolutionary equations, which is done by using the theory of extrapolation spaces.
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Evolutionary equations and constraints: Maxwell equations [PDF]
Journal of Mathematical Physics, 2019 By fixing a reference frame in spacetime, it is possible to split the Euler-Lagrange equations associated with a degenerate Lagrangian into purely evolutionary equations and constraints on the allowed Cauchy data with respect to the notion of space and time associated with the given reference frame.
F. M. Ciaglia +3 more
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Solution Theory for Evolutionary Equations [PDF]
, 2021 AbstractIn this chapter, we shall discuss and present the first major result of the manuscript: Picard’s theorem on the solution theory for evolutionary equations which is the main result of Picard (A structural observation for linear material laws in classical mathematical physics. In Mathematical Methods in the Applied Sciences, vol 32, 2009, pp 1768–
Christian Seifert +2 more
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Exponential Stability of Evolutionary Equations [PDF]
, 2021 AbstractIn this chapter we study the exponential stability of evolutionary equations. Roughly speaking, exponential stability of a well-posed evolutionary equation $$\displaystyle \left (\partial _{t,\nu }M(\partial _{t,\nu })+A\right )U=F $$ ∂
Christian Seifert +2 more
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, 2022 This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required ...
Seifert, Christian +2 more
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Non-Autonomous Evolutionary Equations [PDF]
, 2021 AbstractPreviously, we focussed on evolutionary equations of the form $$\displaystyle \left (\overline {\partial _{t,\nu }M(\partial _{t,\nu })+A}\right )U=F. $$ ∂
Christian Seifert +2 more
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A Schrödinger Equation for Evolutionary Dynamics
Quantum Reports, 2023 We establish an analogy between the Fokker–Planck equation describing evolutionary landscape dynamics and the Schrödinger equation which characterizes quantum mechanical particles, showing that a population with multiple genetic traits evolves analogously to a wavefunction under a multi-dimensional energy potential in imaginary time.
Ao, Vi D. +7 more
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The Price equation and evolutionary epidemiology
Philosophical Transactions of the Royal Society B: Biological Sciences, 2020 The Price equation has found widespread application in many areas of evolutionary biology, including the evolutionary epidemiology of infectious diseases. In this paper, we illustrate the utility of this approach to modelling disease evolution by first deriving a version of Price’s equation that can be applied in continuous time and to populations with
Day, Troy +3 more
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