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Volume 26, Issue 1
Global Existence and Uniqueness of Solutions to Evolution p-Laplacian Systems with Nonlinear Sources

Yingjie Wei & Wenjie Gao

DOI: 10.4208/jpde.v26.n1.1

J. Part. Diff. Eq., 26 (2013), pp. 1-13.

Published online: 2013-03

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  • Abstract

This paper presents the global existence and uniqueness of the initial and boundary value problem to a system of evolution p-Laplacian equations coupled with general nonlinear terms. The authors use skills of inequality estimation and themethod of regularization to construct a sequence of approximation solutions, hence obtain the global existence of solutions to a regularized system. Then the global existence of solutions to the system of evolution p-Laplacian equations is obtained with the application of a standard limiting process. The uniqueness of the solution is proven when the nonlinear terms are local Lipschitz continuous.

  • Keywords

Global existence uniqueness degenerate p-Laplacian systems

  • AMS Subject Headings

35A01, 35A02, 35G55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

weiyj@jlu.edu.cn (Yingjie Wei)

wjgao@jlu.edu.cn (Wenjie Gao)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-26-1, author = {Wei , Yingjie and Gao , Wenjie}, title = {Global Existence and Uniqueness of Solutions to Evolution p-Laplacian Systems with Nonlinear Sources}, journal = {Journal of Partial Differential Equations}, year = {2013}, volume = {26}, number = {1}, pages = {1--13}, abstract = {

This paper presents the global existence and uniqueness of the initial and boundary value problem to a system of evolution p-Laplacian equations coupled with general nonlinear terms. The authors use skills of inequality estimation and themethod of regularization to construct a sequence of approximation solutions, hence obtain the global existence of solutions to a regularized system. Then the global existence of solutions to the system of evolution p-Laplacian equations is obtained with the application of a standard limiting process. The uniqueness of the solution is proven when the nonlinear terms are local Lipschitz continuous.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v26.n1.1}, url = {http://global-sci.org/intro/article_detail/jpde/5149.html} }
TY - JOUR T1 - Global Existence and Uniqueness of Solutions to Evolution p-Laplacian Systems with Nonlinear Sources AU - Wei , Yingjie AU - Gao , Wenjie JO - Journal of Partial Differential Equations VL - 1 SP - 1 EP - 13 PY - 2013 DA - 2013/03 SN - 26 DO - http://doi.org/10.4208/jpde.v26.n1.1 UR - https://global-sci.org/intro/article_detail/jpde/5149.html KW - Global existence KW - uniqueness KW - degenerate KW - p-Laplacian systems AB -

This paper presents the global existence and uniqueness of the initial and boundary value problem to a system of evolution p-Laplacian equations coupled with general nonlinear terms. The authors use skills of inequality estimation and themethod of regularization to construct a sequence of approximation solutions, hence obtain the global existence of solutions to a regularized system. Then the global existence of solutions to the system of evolution p-Laplacian equations is obtained with the application of a standard limiting process. The uniqueness of the solution is proven when the nonlinear terms are local Lipschitz continuous.

Yingjie Wei & Wenjie Gao. (2019). Global Existence and Uniqueness of Solutions to Evolution p-Laplacian Systems with Nonlinear Sources. Journal of Partial Differential Equations. 26 (1). 1-13. doi:10.4208/jpde.v26.n1.1
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