Vibrations of Elastic Strings: Mathematical Aspects, Part Two

By L. A. Medeiros, J. Límaco, S. B. Menezes. 2002

70 citations recorded by the source corpus.

AbstractDedicated to Professor Jacque-Louis Lions on the occasion of his 70th birthday We consider a mixed problem for the operator $$\hat Lu\left( {x,t} \right) = \frac{{\partial ^2 u}}{{\partial t^2 }} - \left( {a\left( t \right) + b\left( t \right)\int_{\alpha \left( t \right)}^{\beta \left( t \right)} {\left( {\frac{{\partial u}}{{\partial x}}} \right)} ^2 dx} \right)\frac{{\partial ^2 u}}{{\partial x^2 }}$$ in a noncylindrical domain $$\widehat Q$$ . We obtain local solution in t. When we add a viscosity we obtain a global solution. We also investigate the asymptotic behavior of the energy.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/a51f08ea01404d1126062c5e01212070e747bf3e

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In Applied Mathematics

1. Francisco Júlio S. A. Corrêa
2. Michel Chipot

In Computational Theory and Mathematics

1. Francisco Júlio S. A. Corrêa
2. Michel Chipot
3. Roland Becker
4. Rolf Rannacher

Citations in the corpus

• Boundary layer solutions to functional elliptic equations (2009, background): “For an account to these issues we refer to [3]–[8], [9]–[11], [16], [19], [21] and [24].”