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Fissato lo spazio di Sobolev $H^{1,2}$ come ambiente del problema dinamico per un corpo viscoelastico unidimensionale si dimostra un teorema di unicità per la classe delle funzioni di rilassamento convesse. Si fa inoltre vedere come tale unicità sia strettamente legata allo spazio ambiente considerato.

Dissipatività ed esistenza per il problema dinamico unidimensionale della viscoelasticità lineare

Giorgio Vergara Caffarelli (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa nota si completa la studio (iniziato in [1]) della caratterizzazione delle funzioni di rilassamento per le quali il problema dinamico della viscoelasticità lineare, con condizioni di spostamento nullo agli estremi, risulta ben posto nello spazio di Sobolev $H^{1,2}$ . Precisamente, per un'opportuna classe di sollecitazioni esterne, si dimostra l'esistenza della soluzione, se le funzioni di rilassamento sono positive, convesse ed hanno il modulo di elasticità all'equilibrio strettamente maggiore...

Distinguishing example for the Tillmann product of distributions

Jiří Jelínek (1990)

Commentationes Mathematicae Universitatis Carolinae

Distribution semigroups on $k_{1}$

M. Mijatović, S. Pilipović (2003)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

Distributional and entire solutions of linear functional differential equations.

Wiener, Joseph (1982)

International Journal of Mathematics and Mathematical Sciences

Distributional boundary values and the tempered ultra-distributions

Richard D. Carmichael (1976)

Rendiconti del Seminario Matematico della Università di Padova

Distributional boundary values in $𝔇_{L^{p}}^{'}$ . III

Richard D. Carmichael (1972)

Rendiconti del Seminario Matematico della Università di Padova

Distributional boundary values in $𝔇_{L^{p}}^{'}$ (IV)

Richard D. Carmichael (1980)

Rendiconti del Seminario Matematico della Università di Padova

Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation

Dariusz Idczak (1998)

Czechoslovak Mathematical Journal

We give characterizations of the distributional derivatives $D^{1, 1}$ , $D^{1, 0}$ , $D^{0, 1}$ of functions of two variables of locally finite variation. Then we use these results to prove the existence theorem for the hyperbolic equation with a nonhomogeneous term containing the distributional derivative determined by an additive function of an interval of finite variation. An application of the above theorem to a hyperbolic equation with an impulse effect is also given.

Distributional solutions in information theory, I

A. Kamiński, Pl. Kannappan, J. Mikusiński (1979)

Annales Polonici Mathematici

Distributional solutions in information theory, II

A. Kamiński, Pl. Kannappan (1980)

Annales Polonici Mathematici

Distributionally regulated functions

Jasson Vindas, Ricardo Estrada (2007)

Studia Mathematica

We study the class of distributions in one variable that have distributional lateral limits at every point, but which have no Dirac delta functions or derivatives at any point, the "distributionally regulated functions." We also consider the related class where Dirac delta functions are allowed. We prove several results on the boundary behavior of functions of two variables F(x,y), x ∈ ℝ, y>0, with F(x,0⁺) = f(x) distributionally, both near points where the distributional point value exists and...

Distributionen mit Werten in topologischen Vektorräumen I.

Reinhold Meise, K.-D. Bierstedt (1973)

Manuscripta mathematica

Distributionen mit Werten in topologischen Vektorräumen II.

Reinhold Meise, K.-D. Bierstedt (1973)

Manuscripta mathematica

Distributions that are functions

Ricardo Estrada (2010)

Banach Center Publications

It is well-known that any locally Lebesgue integrable function generates a unique distribution, a so-called regular distribution. It is also well-known that many non-integrable functions can be regularized to give distributions, but in general not in a unique fashion. What is not so well-known is that to many distributions one can associate an ordinary function, the function that assigns the distributional point value of the distribution at each point where the value exists, and that in many cases...

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