Parabolic problems in generalized Sobolev spaces

<p style='text-indent:20px;'>We consider a general inhomogeneous parabolic initial-boundary value problem for <inline-formula><tex-math id="M1">\begin{document}$ 2b $\end{document}</tex-math></inline-formula>-parabolic differential equation given in finite multidimensional cylinder. We investigate the solvability of this some generalized anisotropic Sobolev spaces. They are parametrized with pair positive numbers id="M2">\begin{document}$ s $\end{document}</tex-math></inline-formula> and id="M3">\begin{document}$ s/(2b) function id="M4">\begin{document}$ \varphi:[1,\infty)\to(0,\infty) that varies slowly at infinity. The parameter id="M5">\begin{document}$ \varphi characterizes subordinate regularity distributions respect to power by number parameters. prove operator corresponding is an isomorphism on appropriate pairs these As application, we give theorem local solution problem. also obtain sharp sufficient conditions under which chosen derivatives continuous set.</p>