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  • 1
    Online Resource
    Online Resource
    Berlin [u.a.] : Springer
    Part of " Lecture notes in mathematics"
    Keywords: Abelsche Integralgleichung ; Abelsche Integralgleichung
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource
    ISBN: 9783540536680 , 9783540469490
    Series Statement: Lecture notes in mathematics 1461
    DDC: 515
    Language: English
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Annali di matematica pura ed applicata 149 (1987), S. 393-409 
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Sunto Nel presente lavoro consideriamo il problema di Cauchy non ben posto ut= (a(x)ux)x, x∈(0, l), t∈(0, T), u(0, t)=ϕ(t), ux(0, t)=0, 0≦t≦T. Supponiamo che a sia misurabile e limitato inferiormente e superiormente da constanti positive. Introduciamo delle limitazioni a priori su u e dimostriamo la dipendenza continua di u rispetto al dato ϕ sia in (0, l)×(0, T) (di tipo hölderiano) sia per x=l (di tipo logaritmico). Consideriamo, inoltre, la dipendenza continua di u da a.
    Notes: Summary In this paper we study the noncharacteristic Cauchy problem, ut−(a(x)ux)x=0, x∈(0, l), t∈.(0, T], u(0, t)=ϕ(t), ux(0,t)=0, 0≦t≦T, assuming only L∞ for a. In the case of weak a priori bounds on u, we derive stability estimates on u of Hölder type in the interior and of logarithmic type at the boundary. Also the continuous dependence on a is considered.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Annali di matematica pura ed applicata 156 (1990), S. 381-404 
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Sunto Nel presente lavoro consideriamo un problema inverso, connesso a questioni di elettrocardiologia, relativo a un potenziale di doppio strato obliquo logaritmico, u, portato da una curva piana Γ. Il problema consiste nel determinare Γ conoscendo u sulla frontiera di un dominio T contenente Γ. Il problema non è ben posto secondo Hadamard. Introduciamo delle limitazioni a priori su Γ e dimostriamo alcuni risultati di stabilità.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    ISSN: 0170-4214
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the non-characteristic Cauchy problem ut-a(x)uxx-b(x)ux-c(x)u = 0, x ∊ (0, l), t ∊ I, u(0, t) = ϕ(t), ux(0, t) = 0, t ∊ I, where I = ∝ or I = ∝+ and u(x, 0) = 0, x ∊ [0, l], in the case I = ∝+. Assuming an a priori bound for ‖u(l,.)‖L2, we derive the exact Hölder type dependence of on ‖u(x,.)‖L2 on ‖ϕ‖L2.
    Type of Medium: Electronic Resource
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