论文标题
全球存在和抗抛物线方程的解决方案，涉及分数$ p（x）$ - laplacian
Global existence and blow-up of solutions for a parabolic equation involving the fractional $p(x)$-Laplacian
论文作者
论文摘要
在本文中，我们考虑了一个非本地扩散方程，涉及$ p（x）$ - laplacian，具有可变指数类型的非线性。采用亚分差方法，我们确定了本地解决方案的存在。通过将潜在的井理论与Nehari歧管相结合，我们获得了全球解决方案的存在和有限的解决方案的时间。此外，我们研究了一些变化的指数lebesgue空间，随着时间的流逝，全球解决方案的渐近稳定性。
In this paper, we consider a non-local diffusion equation involving the fractional $p(x)$-Laplacian with nonlinearities of variable exponent type. Employing the sub-differential approach we establish the existence of local solutions. By combining the potential well theory with the Nehari manifold, we obtain the existence of global solutions and finite time blow-up of solutions. Moreover, we study the asymptotic stability of global solutions as time goes to infinity in some variable exponent Lebesgue spaces.
