Abstract
In this section we shall discuss nonlinear problems. We are interested in smooth solutions. There is no general theory for nonlinear differential equations available. Instead, we ask the following questions. Assume that we know a solution U for a particular set of data. Is the problem still solvable if we make small perturbations of the data? Does the solution depend continuously on the perturbation, i.e., do small perturbations in the data generate small changes in the solution?
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© 2001 Springer Basel AG
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Kreiss, HO., Busenhart, H.U. (2001). Nonlinear Problems. In: Time-dependent Partial Differential Equations and Their Numerical Solution. Lectures in Mathematics. ETH Zürich. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8229-3_4
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DOI: https://doi.org/10.1007/978-3-0348-8229-3_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-6125-9
Online ISBN: 978-3-0348-8229-3
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