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Volume 20, Issue 1
Global Solutions to an Initial Boundary Value Problem for the Mullins Equation

Alber Hans-Dieter & Peicheng Zhu

J. Part. Diff. Eq., 20 (2007), pp. 30-44.

Published online: 2007-02

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  • Abstract

In this article we study the global existence of solutions to an initial boundary value problem for the Mullins equation which describes the groove development at the grain boundaries of a heated polycrystal, both the Dirichlet and the Neumann boundary conditions are considered. For the classical solution we also investigate the large time behavior, it is proved that the solution converges to a constant, in the L^∞(Ω)-norm, as time tends to infinity.

  • Keywords

Mullins equation initial boundary value problem global solutions

  • AMS Subject Headings

35D10 35Q80.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-20-30, author = {Alber Hans-Dieter and Peicheng Zhu }, title = {Global Solutions to an Initial Boundary Value Problem for the Mullins Equation}, journal = {Journal of Partial Differential Equations}, year = {2007}, volume = {20}, number = {1}, pages = {30--44}, abstract = {

In this article we study the global existence of solutions to an initial boundary value problem for the Mullins equation which describes the groove development at the grain boundaries of a heated polycrystal, both the Dirichlet and the Neumann boundary conditions are considered. For the classical solution we also investigate the large time behavior, it is proved that the solution converges to a constant, in the L^∞(Ω)-norm, as time tends to infinity.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5291.html} }
TY - JOUR T1 - Global Solutions to an Initial Boundary Value Problem for the Mullins Equation AU - Alber Hans-Dieter & Peicheng Zhu JO - Journal of Partial Differential Equations VL - 1 SP - 30 EP - 44 PY - 2007 DA - 2007/02 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5291.html KW - Mullins equation KW - initial boundary value problem KW - global solutions AB -

In this article we study the global existence of solutions to an initial boundary value problem for the Mullins equation which describes the groove development at the grain boundaries of a heated polycrystal, both the Dirichlet and the Neumann boundary conditions are considered. For the classical solution we also investigate the large time behavior, it is proved that the solution converges to a constant, in the L^∞(Ω)-norm, as time tends to infinity.

Alber Hans-Dieter and Peicheng Zhu . (2007). Global Solutions to an Initial Boundary Value Problem for the Mullins Equation. Journal of Partial Differential Equations. 20 (1). 30-44. doi:
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