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The Fourier method for abstract equations. (La méthode de Fourier pour des équations abstraites.) (French) Zbl 0885.35022

Using a spectral result of the reviewer and S. Sburlan [An. Univ. “Ovidius” Constanta, Ser. Mat. 2, 188-200 (1994; Zbl 0863.46011)], the author studies by the Fourier method the existence and regularity of solutions for first-order abstract differential equations. Applications to the heat equation are also given.

MSC:

35C10 Series solutions to PDEs
34G10 Linear differential equations in abstract spaces

Citations:

Zbl 0863.46011
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References:

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[4] Nečas, J., “Les méthodes directes en théorie des équations elliptiques”, Masson et Academia, Pariset Prague, 1967 · Zbl 1225.35003
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[6] Yosida, Y., “Functional Analysis”, Springer-Verlag, 1978 · Zbl 0365.46001
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