论文标题
对于半连接伪抛物方程的全球解决方案的存在
Existence of global solutions to a semilinear pseudo-parabolic equation
论文作者
论文摘要
在本文中，我们考虑了一个半线性伪抛物线热方程，其非线性是对数和多项式函数的产物。在这里，我们证明了对任意维度$ n \ geq 1 $和功率索引$ p> 1 $的全球解决方案的存在。该溶液的渐近行为已在不同的能量水平上解决。此外，我们证明了全球解决方案确实以指数率衰减。最后，提供了足够的条件，在该条件下发生了解决方案。
In this article, we consider a semilinear pseudo parabolic heat equation with the nonlinearity which is the product of logarithmic and polynomial functions. Here we prove the global existence of solution to the problem for arbitrary dimension $n \geq 1$ and power index $p>1$. Asymptotic behaviour of the solution has been addressed at different energy levels. Moreover, we prove that the global solution indeed decays with an exponential rate. Finally, sufficient conditions are provided under which blow up of solutions take place.
