Titlebook: Distribution Theory Applied to Differential Equations; Adina Chirilă,Marin Marin,Andreas Öchsner Book 2021 The Editor(s) (if applicable) a

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Differential Equations in Distributions,discussed in the framework of the theory of distributions. Hyperbolic, parabolic and elliptic partial differential equations are solved by means of the Fourier transform. The Cauchy problem is discussed.

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Variational Problems,l formulations of the Stokes system, the elasticity system and the plate equation. Then we discuss the approximation of variational problems by means of the Galerkin method and by means of the finite element method.

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https://doi.org/10.1007/978-3-030-53797-5a approximation and the principal section of a maximal monotone operator. A stability result is shown for the solution of the Cauchy problem associated to an evolution equation based on the inequality of Gronwall.

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The Variational Approach to Fracturediscussed in the framework of the theory of distributions. Hyperbolic, parabolic and elliptic partial differential equations are solved by means of the Fourier transform. The Cauchy problem is discussed.

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https://doi.org/10.1007/978-1-349-00441-6l formulations of the Stokes system, the elasticity system and the plate equation. Then we discuss the approximation of variational problems by means of the Galerkin method and by means of the finite element method.

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https://doi.org/10.1007/978-1-349-00441-6utions operating continuously on . by convolution and such that the Fourier transform maps convolution products into the product of the corresponding Fourier transforms. So we present the space . and its properties.