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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 $E(0)<d.$ 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} }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 $E(0)<d.$ Then using additional conditions on initial data, these results are enlarged at critical case $E(0)=d$ and arbitrarily positive case $E(0)>0.$