A weighted Sobolev space theory for the diffusion-wave equations with time-fractional derivatives on $ C^{1} $ domains
A weighted Sobolev space theory for the diffusion-wave equations with time-fractional derivatives on $ C^{1} $ domains
<p style='text-indent:20px;'>We introduce a weighted <inline-formula><tex-math id="M2">\begin{document}$ L_{p} $\end{document}</tex-math></inline-formula>-theory (<inline-formula><tex-math id="M3">\begin{document}$ p>1 $\end{document}</tex-math></inline-formula>) for the time-fractional diffusion-wave equation of the type <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \partial_{t}^{\alpha}u(t,x) = a^{ij}(t,x)u_{x^{i}x^{j}}(t,x)+f(t,x), \quad t>0, x\in \Omega, \end{equation*} $\end{document} </tex-math></disp-formula> <p style='text-indent:20px;'>where <inline-formula><tex-math id="M4">\begin{document}$ \alpha\in (0,2) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ \partial_{t}^{\alpha} $\end{document}</tex-math></inline-formula> denotes …