Problems that are considered in this book model various mechanical phenomena, especially from rod theory and viscoelasticity. Differential equations that arise have coefficients which are not smooth, can be even distributions (Dirac delta and Heaviside functions), and some equations are coupled with fractional differential equations. This is why one has to go beyond classical spaces and look for solutions within generalized function spaces such as spaces of distributions, Sobolev spaces and Colombeau's generalized functions. Different kinds of techniques are presented and afterwards are employed to show existence and uniqueness of solutions.
Problems that are considered in this book model various mechanical phenomena, especially from rod theory and viscoelasticity. Differential equations that arise have coefficients which are not smooth, can be even distributions (Dirac delta and Heaviside functions), and some equations are coupled with fractional differential equations. This is why one has to go beyond classical spaces and look for solutions within generalized function spaces such as spaces of distributions, Sobolev spaces and Colombeau's generalized functions. Different kinds of techniques are presented and afterwards are employed to show existence and uniqueness of solutions.
This book presents the idea of zero-range potentials and shows the limitations of the point models used in structural mechanics. It also offers specific examples from the theory of generalized...
The International Symposium on Generalized Functions and Their Applications was organized by the Department of Mathematics, Banaras Hindu University, and held December 23-26, 1991, on the occasion of...
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