Geodesic
On the partial boundary value condition basing on the diffusion coefficient
Filomat, Tome 37 (2023) no. 18, p. 5979

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DOI

The paper follows with interest in a nonlinear parabolic equation coming from the electrorheological fluid ut = div(a(x)|∇u|p(x)−2∇u) + XN i=1 ∂bi(u, x, t) ∂xi with a(x) being positive in Ω. We study the well-posedness problem of the equation under the condition bi(·, x, t) = 0 on the partial boundary ∂Ω Σ1 for every i = 1, 2, · · · ,N, where Σ1 = {x ∈ ∂Ω : a(x) > 0}. The stability of the weak solutions is obtained only basing on a partial boundary value condition u(x, t) = 0, (x, t) ∈ Σ1 × (0, T).
DOI : 10.2298/FIL2318979O
Classification : 35K55, 35K92, 35K65, 35R35
Keywords: Electrorheological, diffusion coefficient, partial boundary condition, stability 
Qitong Ou. On the partial boundary value condition basing on the diffusion coefficient. Filomat, Tome 37 (2023) no. 18, p. 5979 . doi: 10.2298/FIL2318979O
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     author = {Qitong Ou},
     title = {On the partial boundary value condition basing on the diffusion coefficient},
     journal = {Filomat},
     pages = {5979 },
     year = {2023},
     volume = {37},
     number = {18},
     doi = {10.2298/FIL2318979O},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2318979O/}
}
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