The entropy solution of a reaction–diffusion equation on an unbounded domain
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Inequalities and Applications"
DOI: 10.1186/s13660-019-1956-3
Abstract: The degenerate parabolic equations from the reaction–diffusion problems are considered on an unbounded domain Ω⊂RN$\varOmega\subset\mathbb {R}^{N}$. It is expected that only a partial boundary should be imposed the homogeneous boundary value, but how to give… read more here.
Keywords: partial boundary; reaction diffusion; unbounded domain;
The well-posedness of an anisotropic parabolic equation based on the partial boundary value condition
Sign Up to like & getrecommendations! Published in 2017 at "Boundary Value Problems"
DOI: 10.1186/s13661-017-0899-1
Abstract: Consider the anisotropic parabolic equation with the variable exponent ut=∑i=1N(ai(x)|uxi|pi(x)−2uxi)xi,$$ {u_{t}}=\sum_{i=1}^{N} \bigl(a_{i}(x)|u_{x_{i}}|^{p_{i}(x)-2}u_{x_{i}} \bigr)_{x _{i}}, $$ with ai(x)$a_{i}(x)$, pi(x)∈C1(Ω‾)$p_{i}(x)\in C^{1}(\overline{\Omega})$, pi(x)>1$p_{i}(x)>1$, ai(x)≥0$a_{i}(x)\geq0$. If some of {ai(x)}$\{a_{i}(x)\}$ are degenerate on the boundary, a partial boundary value condition… read more here.
Keywords: value condition; anisotropic parabolic; value; boundary value ... See more keywords