Volume 22, Issue 1
Traveling Wave Solutions to the Three-dimensional Nonlinear Viscoelastic System

Aihua Chen

J. Part. Diff. Eq., 22 (2009), pp. 42-56.

Published online: 2009-02

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  • Abstract

In this paper, we establish the existence of traveling wave solutions to the nonlinear three-dimensional viscoelastic system exhibiting long range memory. Under certain hypotheses, if the speed of propagation is between the speeds determined by the equilibrium and instantaneous elastic tensors, then the system has nontrivial traveling wave solutions. Moreover, the system has only trivial traveling wave solution in some cases.

  • Keywords

Nonlinear viscoelastic system instantaneous elastic tensor equilibrium elastic tensor upstream condition strongly elliptic condition

  • AMS Subject Headings

35Q72 45K05 74J30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-22-42, author = {}, title = {Traveling Wave Solutions to the Three-dimensional Nonlinear Viscoelastic System}, journal = {Journal of Partial Differential Equations}, year = {2009}, volume = {22}, number = {1}, pages = {42--56}, abstract = {

In this paper, we establish the existence of traveling wave solutions to the nonlinear three-dimensional viscoelastic system exhibiting long range memory. Under certain hypotheses, if the speed of propagation is between the speeds determined by the equilibrium and instantaneous elastic tensors, then the system has nontrivial traveling wave solutions. Moreover, the system has only trivial traveling wave solution in some cases.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5246.html} }
TY - JOUR T1 - Traveling Wave Solutions to the Three-dimensional Nonlinear Viscoelastic System JO - Journal of Partial Differential Equations VL - 1 SP - 42 EP - 56 PY - 2009 DA - 2009/02 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5246.html KW - Nonlinear viscoelastic system KW - instantaneous elastic tensor KW - equilibrium elastic tensor KW - upstream condition KW - strongly elliptic condition AB -

In this paper, we establish the existence of traveling wave solutions to the nonlinear three-dimensional viscoelastic system exhibiting long range memory. Under certain hypotheses, if the speed of propagation is between the speeds determined by the equilibrium and instantaneous elastic tensors, then the system has nontrivial traveling wave solutions. Moreover, the system has only trivial traveling wave solution in some cases.

Aihua Chen . (2019). Traveling Wave Solutions to the Three-dimensional Nonlinear Viscoelastic System. Journal of Partial Differential Equations. 22 (1). 42-56. doi:
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