GENERALIZED SOLUTIONS FOR THE EULER–BERNOULLI MODEL WITH ZENER VISCOELASTIC FOUNDATIONS AND DISTRIBUTIONAL FORCES

DOI10.1142/S0219530513500176zbMath1275.35071arXiv1102.2148OpenAlexW2163251769MaRDI QIDQ4916145

Sanja Konjik, Günther Hörmann, Ljubica Oparnica

Publication date: 19 April 2013

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.2148

zbMATH Keywords

energy estimatesleft Riemann-Liouville fractional derivative

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Variational methods applied to PDEs (35A15) Fractional derivatives and integrals (26A33) Linear constitutive equations for materials with memory (74D05) Weak solutions to PDEs (35D30) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) PDEs in connection with mechanics of deformable solids (35Q74) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09)

Related Items (6)

Stochastic parabolic equations with singular potentials ⋮ An existence and uniqueness result about algebras of Schwartz distributions ⋮ Vibration modes of the Euler-Bernoulli beam equation with singularities ⋮ Ordinary differential equations with singular coefficients: an intrinsic formulation with applications to the Euler-Bernoulli beam equation ⋮ Elastic and viscoelastic foundations: a review on linear and nonlinear vibration modeling and applications ⋮ The Euler-Bernoulli equation with distributional coefficients and forces

Cites Work

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• On Mittag-Leffler-type functions in fractional evolution processes
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• Topological structures in Colombeau algebras: Investigation of the duals of \(\mathcal G_c(\Omega)\), \(\mathcal G(\Omega)\) and \(\mathcal G_{\mathcal S}(\mathbb R^n)\)
• Distributional solution concepts for the Euler–Bernoulli beam equation with discontinuous coefficients
• Generalized Solutions to the Korteweg–de Vries and the Regularized Long-Wave Equations
• On applications of generalized functions to the analysis of Euler-Bernoulli beam-columns with jump discontinuities
• On nonuniform Euler-Bernoulli and Timoshenko beams with jump discontinuities: Application of distribution theory
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