Fritz John pp 411-424 | Cite as

Numerical Solution of Problems which are not Well Posed in the Sense of Hadamardd

  • Fritz John
Part of the Contemporary Mathematicians book series (CM)


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


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  1. [1]
    Mauro PiconeSul calcolo delle funzioni olomorfe di una, yariabile complessa. Studies in Mathematics presented o Richard von Mises (1954) pp 118–126.Google Scholar
  2. [2]
    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– 477Google Scholar
  3. [3]
    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.Google Scholar
  4. [4]
    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,Google Scholar
  5. [5]
    The Dirichlet problem for the wave equation, Annali di mat pura ed applicata Serie IV, v. 46 (1958) pp. 155–182.Google Scholar
  6. [6]
    F. John A note on improper problems in partial di fferential equations. Communications on Pure and Applied Mathematics, v. 8 (1955) pp. 591–594,CrossRefGoogle Scholar
  7. [7]
    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,Google Scholar
  8. [8]
    On linear partial differential equations with analytic coefficients (Unique continuation of data), Comm. Pure and Appl. Math. v. 2 (1949) pp 209–253Google Scholar
  9. [9]
    E. M. Landis On some properties of solutions of elliptic equations Dokl Akad Nauk SSSR (N S ) 107 (1956) pp 640–643Google Scholar
  10. [10]
    L. Nirenberg Uniqueness of Cauchy problems for differential equations with constant leading, coefficients Comm Pure and Appl Math v 10 (1957) pp 89–105CrossRefGoogle Scholar
  11. [11]
    R. Courant and D. Hilbert Methoden der mathematischen Physik Springer Verlag,1937CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Fritz John
    • 1
  1. 1.New York UniversityUSA

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