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Volume 38, Issue 3
Definite Condition of the Evolutionary $\vec{p}(x)$−Laplacian Equation

Huashui Zhan & Zhaosheng Feng

DOI: 10.4208/ata.OA-2021-0029

Anal. Theory Appl., 38 (2022), pp. 297-321.

Published online: 2022-07

[An open-access article; the PDF is free to any online user.]

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  • Abstract

For the nonlinear degenerate parabolic equations, how to find an appropriate boundary value condition to ensure the well-posedness of weak solution has been an interesting and challenging problem. In this paper, we develop the general characteristic function method to study the stability of weak solutions based on a partial boundary value condition.

  • Keywords

Definite condition, stability, general characteristic function method, weak solution, Laplacian equation.

  • AMS Subject Headings

35B35, 35D30, 35K55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-38-297, author = {Zhan , Huashui and Feng , Zhaosheng}, title = {Definite Condition of the Evolutionary $\vec{p}(x)$−Laplacian Equation}, journal = {Analysis in Theory and Applications}, year = {2022}, volume = {38}, number = {3}, pages = {297--321}, abstract = {

For the nonlinear degenerate parabolic equations, how to find an appropriate boundary value condition to ensure the well-posedness of weak solution has been an interesting and challenging problem. In this paper, we develop the general characteristic function method to study the stability of weak solutions based on a partial boundary value condition.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2021-0029}, url = {http://global-sci.org/intro/article_detail/ata/20803.html} }
TY - JOUR T1 - Definite Condition of the Evolutionary $\vec{p}(x)$−Laplacian Equation AU - Zhan , Huashui AU - Feng , Zhaosheng JO - Analysis in Theory and Applications VL - 3 SP - 297 EP - 321 PY - 2022 DA - 2022/07 SN - 38 DO - http://doi.org/10.4208/ata.OA-2021-0029 UR - https://global-sci.org/intro/article_detail/ata/20803.html KW - Definite condition, stability, general characteristic function method, weak solution, Laplacian equation. AB -

For the nonlinear degenerate parabolic equations, how to find an appropriate boundary value condition to ensure the well-posedness of weak solution has been an interesting and challenging problem. In this paper, we develop the general characteristic function method to study the stability of weak solutions based on a partial boundary value condition.

Huashui Zhan & Zhaosheng Feng. (2022). Definite Condition of the Evolutionary $\vec{p}(x)$−Laplacian Equation. Analysis in Theory and Applications. 38 (3). 297-321. doi:10.4208/ata.OA-2021-0029
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