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Volume 25, Issue 2
Global Solvability in Thermoelasticity with Second Sound on the Semi-axis

Yuxi Hu

DOI: 10.4208/jpde.v25.n2.3

J. Part. Diff. Eq., 25 (2012), pp. 139-170.

Published online: 2012-06

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  • Abstract

In this paper, we consider initial boundary value problem for the equations of one-dimensional nonlinear thermoelasticity with second sound in R^+. First, we derive decay rates for linear systems which, in fact, is a hyperbolic systems with a damping term. Then, using this linear decay rates, we get L^1 and L^∞ decay rates for nonlinear systems. Finally, combining with L^2 estimates and a local existence theorem, we prove a global existence and uniqueness theorem for small smooth data.

  • Keywords

Second sound linear decay rates semi-axis global solution

  • AMS Subject Headings

35L50, 74F05, 74H20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

huyuxi@sjtu.edu.cn (Yuxi Hu)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-25-139, author = {Hu , Yuxi}, title = {Global Solvability in Thermoelasticity with Second Sound on the Semi-axis}, journal = {Journal of Partial Differential Equations}, year = {2012}, volume = {25}, number = {2}, pages = {139--170}, abstract = {

In this paper, we consider initial boundary value problem for the equations of one-dimensional nonlinear thermoelasticity with second sound in R^+. First, we derive decay rates for linear systems which, in fact, is a hyperbolic systems with a damping term. Then, using this linear decay rates, we get L^1 and L^∞ decay rates for nonlinear systems. Finally, combining with L^2 estimates and a local existence theorem, we prove a global existence and uniqueness theorem for small smooth data.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v25.n2.3}, url = {http://global-sci.org/intro/article_detail/jpde/5180.html} }
TY - JOUR T1 - Global Solvability in Thermoelasticity with Second Sound on the Semi-axis AU - Hu , Yuxi JO - Journal of Partial Differential Equations VL - 2 SP - 139 EP - 170 PY - 2012 DA - 2012/06 SN - 25 DO - http://doi.org/10.4208/jpde.v25.n2.3 UR - https://global-sci.org/intro/article_detail/jpde/5180.html KW - Second sound KW - linear decay rates KW - semi-axis KW - global solution AB -

In this paper, we consider initial boundary value problem for the equations of one-dimensional nonlinear thermoelasticity with second sound in R^+. First, we derive decay rates for linear systems which, in fact, is a hyperbolic systems with a damping term. Then, using this linear decay rates, we get L^1 and L^∞ decay rates for nonlinear systems. Finally, combining with L^2 estimates and a local existence theorem, we prove a global existence and uniqueness theorem for small smooth data.

Hu , Yuxi. (2012). Global Solvability in Thermoelasticity with Second Sound on the Semi-axis. Journal of Partial Differential Equations. 25 (2). 139-170. doi:10.4208/jpde.v25.n2.3
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