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Volume 40, Issue 3
The Characteristics of Solutions to Semilinear Wave Equation with Logarithmic Plus Polynomial Nonlinearities

Md Salik Ahmed & Weipeng Wu

DOI: 10.4208/aam.OA-2024-0011

Ann. Appl. Math., 40 (2024), pp. 262-284.

Published online: 2024-09

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  • Abstract

The semilinear wave equation with logarithmic and polynomial nonlinearities is considered in this paper. By adjusting and using potential well method, we attain the global-in-time existence and infinite time blowup solutions at subcritical initial energy level $E(0)<0.$ Then using additional conditions on initial data, these results are enlarged at critical case $E(0)=d$ and arbitrarily positive case $E(0)>0.$

  • Keywords

Global existence, blowup, logarithmic and polynomial combined nonlinearity, potential well.

  • AMS Subject Headings

35L05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAM-40-262, author = {Ahmed , Md Salik and Wu , Weipeng}, title = {The Characteristics of Solutions to Semilinear Wave Equation with Logarithmic Plus Polynomial Nonlinearities}, journal = {Annals of Applied Mathematics}, year = {2024}, volume = {40}, number = {3}, pages = {262--284}, abstract = {

The semilinear wave equation with logarithmic and polynomial nonlinearities is considered in this paper. By adjusting and using potential well method, we attain the global-in-time existence and infinite time blowup solutions at subcritical initial energy level $E(0)<0.$ Then using additional conditions on initial data, these results are enlarged at critical case $E(0)=d$ and arbitrarily positive case $E(0)>0.$

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2024-0011}, url = {http://global-sci.org/intro/article_detail/aam/23423.html} }
TY - JOUR T1 - The Characteristics of Solutions to Semilinear Wave Equation with Logarithmic Plus Polynomial Nonlinearities AU - Ahmed , Md Salik AU - Wu , Weipeng JO - Annals of Applied Mathematics VL - 3 SP - 262 EP - 284 PY - 2024 DA - 2024/09 SN - 40 DO - http://doi.org/10.4208/aam.OA-2024-0011 UR - https://global-sci.org/intro/article_detail/aam/23423.html KW - Global existence, blowup, logarithmic and polynomial combined nonlinearity, potential well. AB -

The semilinear wave equation with logarithmic and polynomial nonlinearities is considered in this paper. By adjusting and using potential well method, we attain the global-in-time existence and infinite time blowup solutions at subcritical initial energy level $E(0)<0.$ Then using additional conditions on initial data, these results are enlarged at critical case $E(0)=d$ and arbitrarily positive case $E(0)>0.$

Md Salik Ahmed & Weipeng Wu. (2024). The Characteristics of Solutions to Semilinear Wave Equation with Logarithmic Plus Polynomial Nonlinearities. Annals of Applied Mathematics. 40 (3). 262-284. doi:10.4208/aam.OA-2024-0011
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