Abstract
Problems involving differential equations usually come in the following form: we are given an equation for the unknown function u, P(u) = f, on a domain Ω together with some “side” conditions on u. For example, we may require that u assumes certain preassigned values on ∂Ω, or that u is in L 2(Ω), or that u is in class C k in Ω. At first glance, it would seem that any of these extra conditions are quite reasonable, and that one is as good as the other. However, we shall see that this is far from being true, and that whichever additional supplementary conditions one assigns is intimately connected with the form of equation.
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© 1994 Springer Science+Business Media New York
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Smoller, J. (1994). Ill-Posed Problems. In: Shock Waves and Reaction—Diffusion Equations. Grundlehren der mathematischen Wissenschaften, vol 258. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0873-0_1
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DOI: https://doi.org/10.1007/978-1-4612-0873-0_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6929-8
Online ISBN: 978-1-4612-0873-0
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