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Blow-up and global existence for semilinear parabolic systems with space-time forcing terms
Chaos, Solitons & Fractals ( IF 5.3 ) Pub Date : 2021-05-10 , DOI: 10.1016/j.chaos.2021.110982 Ahmad Z. Fino , Mohamed Jleli , Bessem Samet
中文翻译:
具有时空强迫项的半线性抛物系统的爆破和整体存在
更新日期:2021-05-11
Chaos, Solitons & Fractals ( IF 5.3 ) Pub Date : 2021-05-10 , DOI: 10.1016/j.chaos.2021.110982 Ahmad Z. Fino , Mohamed Jleli , Bessem Samet
We investigate the finite time blow-up and global existence of sign-changing solutions to the Cauchy problem for the inhomogeneous semilinear parabolic system with space-time forcing termswhere and . For the finite time blow-up, two cases are discussed under the conditions and . Namely, if or we show that the (mild) solution to the considered system blows up in finite time, while if then a finite time blow-up occurs when . Moreover, if and we show that the solution is global for suitable initial values and .
中文翻译:
具有时空强迫项的半线性抛物系统的爆破和整体存在
我们研究了具有时空强迫项的非均匀半线性抛物系统的柯西问题的有限时间爆炸和符号改变解的整体存在性在哪里 和 。对于有限时间爆炸,在条件下讨论了两种情况 和 。即,如果 或者 我们表明(温和的)解决方案 到考虑的系统会在有限的时间内爆炸,而如果 然后发生有限时间的爆炸 。而且,如果 和 我们表明,对于合适的初始值,解决方案是全局的 。