On classes of well-posedness for quasilinear diffusion equations in the whole space
نویسندگان
چکیده
Well-posedness classes for degenerate elliptic problems in \begin{document}$ {\mathbb R}^N $\end{document} under the form id="M2">\begin{document}$ u = \Delta {{\varphi}}(x,u)+f(x) $\end{document}, with locally (in id="M3">\begin{document}$ $\end{document}) uniformly continuous nonlinearities, are explored. While we particularly interested id="M4">\begin{document}$ L^\infty setting, also investigate about solutions id="M5">\begin{document}$ L^1_{loc} and weighted id="M6">\begin{document}$ L^1 spaces. We give some sufficient conditions order that uniqueness comparison properties hold associated solutions; these expressed terms of moduli continuity id="M7">\begin{document}$ u\mapsto {{\varphi}}(x,u) $\end{document}. Under additional restrictions on dependency id="M8">\begin{document}$ {{\varphi}} id="M9">\begin{document}$ x deduce existence results corresponding data. Moreover, dependence follow readily from claim property. In particular, show a general non-decreasing nonlinearity id="M10">\begin{document}$ {{\varphi}}: R}\mapsto R} space id="M11">\begin{document}$ (endowed id="M12">\begin{document}$ topology) is well-posedness class problem id="M13">\begin{document}$ {{\varphi}}(u)+f(x)
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems - Series S
سال: 2021
ISSN: ['1937-1632', '1937-1179']
DOI: https://doi.org/10.3934/dcdss.2020361