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Volume 29, Issue 1
Existence and Blow-up of Solutions for a Nonlinear Parabolic System with Variable Exponents

Yunzhu Gao & Wenjie Gao

Commun. Math. Res., 29 (2013), pp. 61-67.

Published online: 2021-05

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  • Abstract

In this paper, we study a nonlinear parabolic system with variable exponents. The existence of classical solutions to an initial and boundary value problem is obtained by a fixed point theorem of the contraction mapping, and the blow-up property of solutions in finite time is obtained with the help of the eigenfunction of the Laplace equation and a delicate estimate.

  • Keywords

blow-up, existence, nonlinear parabolic system, variable exponent.

  • AMS Subject Headings

35K15, 35K20, 35K55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-29-61, author = {Yunzhu and Gao and and 18921 and and Yunzhu Gao and Wenjie and Gao and and 18922 and and Wenjie Gao}, title = {Existence and Blow-up of Solutions for a Nonlinear Parabolic System with Variable Exponents}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {29}, number = {1}, pages = {61--67}, abstract = {

In this paper, we study a nonlinear parabolic system with variable exponents. The existence of classical solutions to an initial and boundary value problem is obtained by a fixed point theorem of the contraction mapping, and the blow-up property of solutions in finite time is obtained with the help of the eigenfunction of the Laplace equation and a delicate estimate.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19029.html} }
TY - JOUR T1 - Existence and Blow-up of Solutions for a Nonlinear Parabolic System with Variable Exponents AU - Gao , Yunzhu AU - Gao , Wenjie JO - Communications in Mathematical Research VL - 1 SP - 61 EP - 67 PY - 2021 DA - 2021/05 SN - 29 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19029.html KW - blow-up, existence, nonlinear parabolic system, variable exponent. AB -

In this paper, we study a nonlinear parabolic system with variable exponents. The existence of classical solutions to an initial and boundary value problem is obtained by a fixed point theorem of the contraction mapping, and the blow-up property of solutions in finite time is obtained with the help of the eigenfunction of the Laplace equation and a delicate estimate.

Yunzhu Gao & Wenjie Gao. (2021). Existence and Blow-up of Solutions for a Nonlinear Parabolic System with Variable Exponents. Communications in Mathematical Research . 29 (1). 61-67. doi:
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