Abstract
Problems in partial differential equations usually require that a solution u of the differential equation is to be determined from certain data f. In a well posed problem in the sense of Hadamard u exists for all f of a certain class C s is uniquely determined by f and depends continuously on f. Well posed problems of this type are presented by the classical initial and boundary value problems of mathematical physics Existence of solutions has been established for rather general classes of such problems Considerable progress has also been made in constructing numerical schemes to approximate solutions: these schemes have to be stable in the sense that they furnish approximations which are represented by operators acting on the data f which are bounded uniformly
This research was supported in whole by the United States Air Force under Contract No. AF 49(638) – 161 monitored by the Air Force Office of Scientific Research of the Air Research and Development Command.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Mauro PiconeSul calcolo delle funzioni olomorfe di una, yariabile complessa. Studies in Mathematics presented o Richard von Mises (1954) pp 118–126.
Carlo Pucci Sui problemi di Cauchy non “ben posti” Rend. dell’Accad Naz. dei Lincei (Classe di Sc fis mat. e nat.) serie VIII, v. 18 (1955) pp. 473– 477
Studio col metodo delle differenze di un problema. Di Cauchy relativo ad equazioni a. derivate parziali del secondo ordine di tipo parabolico.Annali della ScuoIa Norm. Sup di Pisa serie III, v. 7 (1953) pp 205–215.
Discussione del problema di Cauchy per Ie equazioni di tipo ellittico. Annali di mat pura ed applicata.Serie IV, v 46 (1958) pp 131–154,
The Dirichlet problem for the wave equation, Annali di mat pura ed applicata Serie IV, v. 46 (1958) pp. 155–182.
F. John A note on improper problems in partial di fferential equations. Communications on Pure and Applied Mathematics, v. 8 (1955) pp. 591–594,
Numerical solution of the equation of heat conduction for preceding times Annali di mat pura ed applicata serie IV, v. 40 (1955) pp 129–142,
On linear partial differential equations with analytic coefficients (Unique continuation of data), Comm. Pure and Appl. Math. v. 2 (1949) pp 209–253
E. M. Landis On some properties of solutions of elliptic equations Dokl Akad Nauk SSSR (N S ) 107 (1956) pp 640–643
L. Nirenberg Uniqueness of Cauchy problems for differential equations with constant leading, coefficients Comm Pure and Appl Math v 10 (1957) pp 89–105
R. Courant and D. Hilbert Methoden der mathematischen Physik Springer Verlag,1937
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer Science+Business Media New York
About this chapter
Cite this chapter
John, F. (1985). Numerical Solution of Problems which are not Well Posed in the Sense of Hadamardd. In: Moser, J. (eds) Fritz John. Contemporary Mathematicians. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-5406-5_32
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5406-5_32
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-5408-9
Online ISBN: 978-1-4612-5406-5
eBook Packages: Springer Book Archive