Geodesic
Degenerating parabolic equations with a variable direction of evolution
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 718-731

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The aim of the paper is to study the solvability in the classes of regular solutions of boundary value problems for differential equations $$ \varphi(t)u_t-\psi(t)\Delta u+c(x,t)u=f(x,t)\quad (x\in\Omega\subset \mathbb{R}^n,\quad 0). $$ A feature of these equations is that the function $\varphi (t)$ in them can arbitrarily change the sign on the segment $[0, T]$, while the function $\psi (t)$ is nonnegative for $t \in [0, T]$. For the problems under consideration, we prove existence and uniqueness theorems.
Keywords: degenerate parabolic equations, boundary value problems, regular solutions, uniqueness.
Mots-clés : variable direction of evolution, existence 
@article{SEMR_2019_16_a85,
     author = {A. I. Kozhanov and E. E. Macievskaya},
     title = {Degenerating parabolic equations with a variable direction of evolution},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {718--731},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a85/}
}
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A. I. Kozhanov; E. E. Macievskaya. Degenerating parabolic equations with a variable direction of evolution. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 718-731. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a85/