Generalized solutions for the Euler-Bernoulli model with distributional forces

被引：7
|
作者：
Hoermann, Guenther [2 ]
Oparnica, Ljubica [1 ]
机构：
[1] Serbian Acad Sci, Inst Math, Belgrade 11000, Serbia
[2] Univ Vienna, Fak Math, A-1090 Vienna, Austria
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 357卷 / 01期
基金：
奥地利科学基金会;
关键词：
Generalized solutions to partial differential equations; Functional analytic methods; Differential equations with discontinuous coefficients; Colombeau generalized functions; Nonlinear theories of generalized functions; DISCONTINUOUS COEFFICIENTS; EQUATIONS; ALGEBRAS;
D O I：
10.1016/j.jmaa.2009.03.069
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves discontinuous, and even distributional, coefficients and right-hand side. The general problem is solved by application of functional analytic techniques to obtain estimates for the solutions to regularized problems. Finally, we prove coherence properties and provide a regularity analysis of the generalized solution. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：142 / 153
页数：12
相关论文
共 50 条
  • [1] GENERALIZED SOLUTIONS FOR THE EULER-BERNOULLI MODEL WITH ZENER VISCOELASTIC FOUNDATIONS AND DISTRIBUTIONAL FORCES
    Hoermann, Guenther
    Konjik, Sanja
    Oparnica, Ljubica
    ANALYSIS AND APPLICATIONS, 2013, 11 (02)
  • [2] The Euler-Bernoulli equation with distributional coefficients and forces
    Blommaert, Robin
    Lazendic, Srdan
    Oparnica, Ljubica
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2022, 123 : 171 - 183
  • [3] The Euler-Bernoulli equation with distributional coefficients and forces[Formula presented]
    Blommaert, Robin
    Lazendić, Srdan
    Oparnica, Ljubica
    Computers and Mathematics with Applications, 2022, 123 : 171 - 183
  • [4] Exact solutions of Euler-Bernoulli beams
    Haider, Jamil Abbas
    Zaman, F. D.
    Lone, Showkat Ahmad
    Anwar, Sadia
    Almutlak, Salmeh A.
    Elseesy, Ibrahim E.
    MODERN PHYSICS LETTERS B, 2023, 37 (33):
  • [5] Noether symmetries and exact solutions of an Euler-Bernoulli beam model
    Fatima, Aeeman
    Mahomed, Fazal M.
    Khalique, Chaudry Masood
    INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2016, 30 (28-29):
  • [6] EXTREMALS OF THE GENERALIZED EULER-BERNOULLI ENERGY AND APPLICATIONS
    Garay, Oscar J.
    JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS, 2008, 12 : 27 - 61
  • [7] Bayesian Updating in the Determination of Forces in Euler-Bernoulli Beams
    Kawano, Alexandre
    Zine, Abdelmalek
    NEW TRENDS IN PARAMETER IDENTIFICATION FOR MATHEMATICAL MODELS, 2018, : 159 - 174
  • [8] GEVREY SOLUTIONS FOR EQUATIONS OF EULER-BERNOULLI TYPE
    TAYLOR, SW
    JOURNAL OF DIFFERENTIAL EQUATIONS, 1991, 92 (02) : 331 - 359
  • [9] Distributional solution concepts for the Euler-Bernoulli beam equation with discontinuous coefficients
    Hoermann, Guenther
    Oparnica, Ljubica
    APPLICABLE ANALYSIS, 2007, 86 (11) : 1347 - 1363
  • [10] On generalized nonlinear Euler-Bernoulli Beam type equations
    Khaldi, Rabah
    Guezane-Lakoud, Assia
    ACTA UNIVERSITATIS SAPIENTIAE-MATHEMATICA, 2018, 10 (01) : 90 - 100
12345