The global Cauchy problem for a vibrating beam equation (Q833293)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The global Cauchy problem for a vibrating beam equation |
scientific article; zbMATH DE number 5593945
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The global Cauchy problem for a vibrating beam equation |
scientific article; zbMATH DE number 5593945 |
Statements
The global Cauchy problem for a vibrating beam equation (English)
0 references
12 August 2009
0 references
The authors investigate the Cauchy problem for an evolution equation of the fourth order in the spatial variable and second order in time. The evolutionary equation models an Euler-Bernoulli vibrating beam with time dependent elastic modulus under a force linear function of the displacement. As a main result, they prove well-posedness of solutions in suitable Sobolev spaces assuming that the coefficient of the shear term decays at the specific rate.
0 references
beam equation
0 references
Euler-Bernoulli vibrating beam
0 references
Cauchy problem
0 references
time dependent elastic modulus
0 references
well-posedness
0 references
0 references
