Ontology type: schema:ScholarlyArticle Open Access: True
2022-05-02
AUTHORS ABSTRACTThis paper is concerned with the well-posedness problem of a doubly degenerate parabolic equation with variable exponents. By the parabolically regularized method, the existence of local solution is proved. Moreover, the trace of u∈W01,1(Ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$u\in W^{1,1}_{0}(\Omega )$\end{document} is generalized to u∈Wloc1,1(Ω)⋂L∞(Ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$u\in W^{1,1}_{\mathrm{loc}}(\Omega )\bigcap L^{\infty}(\Omega )$\end{document} in a rational way. Then, a partial boundary value condition matching up with the stability theorem is found. More... »
PAGES38
http://scigraph.springernature.com/pub.10.1186/s13662-022-03710-y
DOIhttp://dx.doi.org/10.1186/s13662-022-03710-y
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