Abstract
When a physical system is modeled by a “formal” equation of evolution (e. g., a P.D.E. or F.D.E.), often assumptions are made that have little to do with the physics of the system but are made for the convenience of the modeler; that is, they are made so that the formal equation “makes sense.” To a mathematician not interested in applications, such artificial assumptions are as good as any others, and their occasionally disruptive effect on existence, uniqueness, and continuity of solutions (of the formal equation) is an interesting phenomenon, worthy of considerable study. However, to someone interested in applications, such phenomena are irritating rather than interesting, indicating only that a better model is needed. Experience indicates that a physical system does have a unique “motion” for any physically possible initial data and that physical motions are usually in some sense continuously dependent on time; hence, a good mathematical model should also have these properties.
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© 1980 Plenum Press, New York
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Walker, J.A. (1980). Abstract Dynamical Systems and Evolution Equations. In: Dynamical Systems and Evolution Equations. Mathematical Concepts and Methods in Science and Engineering, vol 20. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1036-5_3
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DOI: https://doi.org/10.1007/978-1-4684-1036-5_3
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