The aim of this paper is to study the following time-space fractional diffusion problem $$\begin{aligned} {\left\{ \begin{array}{ll} \displaystyle \partial _t^\beta u+(-\Delta )^\alpha u+(-\Delta )^\alpha \partial _t^\beta u=\lambda f(x,u) +g(x,t) &{}\text{ in } \Omega \times {\mathbb {R}}^{+},\\ u(x,t)=0\ \ &{}\text{ in } ({\mathbb {R}}^N{\setminus }\Omega )\times {\mathbb {R}}^+,\\ u(x,0)=u_0(x)\ &{}\text{ in } \Omega ,\\ \end{array}\right. } \end{aligned}$$ ∂ t β u + ( - Δ ) α u + ( - Δ ) α ∂ t β u = λ f ( x , u ) + g ( x , t ) in Ω × R + , u ( x , t ) = 0 in ( R N \ Ω ) × R + , u ( x , 0 ) = u 0 ( x ) in Ω , where $$\Omega \subset {\mathbb {R}}^N$$ Ω ⊂ R N is a bounded domain with Lipschitz boundary, $$(-\Delta )^{\alpha }$$ ( - Δ ) α is the fractional Laplace operator with $$0<\alpha <1$$ 0 < α < 1 , $$\partial _t^{\beta }$$ ∂ t β is the Riemann-Liouville time fractional derivative with $$0<\beta <1$$ 0 < β < 1 , $$\lambda $$ λ is a positive parameter, $$f:\Omega \times {\mathbb {R}}\rightarrow {\mathbb {R}}$$ f : Ω × R → R is a continuous function, and $$g\in L^2(0,\infty ;L^2(\Omega ))$$ g ∈ L 2 ( 0 , ∞ ; L 2 ( Ω ) ) . Under natural assumptions, the global and local existence of solutions are obtained by applying the Galerkin method. Then, by virtue of a differential inequality technique, we give a decay estimate of solutions. Moreover, the blow-up property of solutions is also investigated.
Under the background that the semiconductor industry receive attention due to the fierce international competition, this paper analyzes the event of Intel's acquisition of Tower Semiconductor, lists the development situation and acquisition objectives of Intel, and analyzes the impact of this acquisition through SWOT. Although this acquisition is in line with Intel's IDM2.0 strategy of developing foundry business and improving manufacturing capacity, due to the limitations of technology, market share and other factors, Intel cannot rely on foundry business for future development and should still take technological innovation as the top priority. At present, there is no paper on the systematic analysis of Intel's acquisition, so the purpose of this paper is to clarify the significance of this acquisition and try to put forward suggestions for Intel's leaders. For Intel, it needs to take technological innovation as the development orientation and further integrate its internal industrial layout in order to stand out in the fierce competition in the semiconductor industry.
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