B¨acklund Transformations are considered referring to partial differential equations, in general. Then, two different models of a rigid linear heat conductor, with and without memory, are considered. Specifically, the Cole-Hopf transformation which relates the linear heat equation to the nonlinear Burgers equation is assumed as a key notion. Then, a generalization is introduced. In particular, a integro-differential type evolution equation which models heat conduction in a material with memory is shown to be related to a nonlinear hyperbolic equation which can be regarded as a hyperbolic generalization of Burgers equation. Notably, the latter admits wave solutions. An overview on application of Baecklund Transformations is provided referring to heat conduction problems.

Baecklund Transformations and Rigid Heat Conduction with Memory / Carillo, Sandra. - STAMPA. - Supplementary(2010), pp. 8-17.

Baecklund Transformations and Rigid Heat Conduction with Memory

CARILLO, Sandra
2010

Abstract

B¨acklund Transformations are considered referring to partial differential equations, in general. Then, two different models of a rigid linear heat conductor, with and without memory, are considered. Specifically, the Cole-Hopf transformation which relates the linear heat equation to the nonlinear Burgers equation is assumed as a key notion. Then, a generalization is introduced. In particular, a integro-differential type evolution equation which models heat conduction in a material with memory is shown to be related to a nonlinear hyperbolic equation which can be regarded as a hyperbolic generalization of Burgers equation. Notably, the latter admits wave solutions. An overview on application of Baecklund Transformations is provided referring to heat conduction problems.
2010
New Trends in Fluid and Solid Models: Proceedings of the International Conference in Honour of Brian Straughan - Supplementary
9789814293211
Baecklund Transformations; Heat CONDUCTION WITH MEMORY
02 Pubblicazione su volume::02a Capitolo o Articolo
Baecklund Transformations and Rigid Heat Conduction with Memory / Carillo, Sandra. - STAMPA. - Supplementary(2010), pp. 8-17.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/190745
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