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A general class of evolutionary equations

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Abstract

Using observable quantities and state variable of a dynamical process, a general evolutionary equation is defined which unifies classical ordinary differential equations, partial differential equations, and hereditary systems of retarded and neutral type. Specific illustrations are given using transmission lines nearest-neighbor coupled at the boundary and the theory of heat transfer in solids. Some spectral theory for linearization of the equations is also discussed.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 2, pp. 268–288, February, 2007.

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Hale, J.K. A general class of evolutionary equations. Ukr Math J 59, 293–314 (2007). https://doi.org/10.1007/s11253-007-0020-5

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Keywords

  • Periodic Orbit
  • Transmission Line
  • Mild Solution
  • Functional Differential Equation
  • Essential Spectrum