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.


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


Zbl 0863.46011
Full Text: DOI Numdam EuDML


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