Geodesic
On the Solvability of Nonlinear Parabolic Functional-Differential
Matematičeskie zametki, Tome 113 (2023) no. 5, pp. 747-763

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The first mixed boundary value problem for a nonlinear functional-differential equation of parabolic type with shifts in the spatial variables is considered. Sufficient conditions are proved under which a nonlinear differential-difference operator is demicontinuous, coercive, and pseudomonotone on the domain of the operator $\partial_t$. Based on these properties, existence theorems for a generalized solution are proved.
Keywords: nonlinear parabolic functional-differential equation, shift operator, pseudomonotone operator on $W$, ellipticity condition. 
@article{MZM_2023_113_5_a10,
     author = {O. V. Solonukha},
     title = {On the {Solvability} of {Nonlinear} {Parabolic} {Functional-Differential}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {747--763},
     publisher = {mathdoc},
     volume = {113},
     number = {5},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_5_a10/}
}
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O. V. Solonukha. On the Solvability of Nonlinear Parabolic Functional-Differential. Matematičeskie zametki, Tome 113 (2023) no. 5, pp. 747-763. http://geodesic.mathdoc.fr/item/MZM_2023_113_5_a10/