Geodesic
On the Well-Posedness of an Initial--Boundary Value Problem for a Degenerate Heat Equation
Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 230-244

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The well-posedness of an initial–boundary value problem for a model parabolic equation with two power-law degeneration lines is studied. Two initial–boundary value problems depending on the degeneracy exponents are stated, and uniqueness and existence theorems are proved. The solutions of these problems are constructed in closed form.
Keywords: parabolic equation with two power degeneration lines, initial–boundary value problem, uniqueness, series, integral representation.
Mots-clés : existence 
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     author = {A. R. Zaynullov and K. B. Sabitov},
     title = {On the {Well-Posedness} of an {Initial--Boundary} {Value} {Problem} for a {Degenerate} {Heat} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a6/}
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A. R. Zaynullov; K. B. Sabitov. On the Well-Posedness of an Initial--Boundary Value Problem for a Degenerate Heat Equation. Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 230-244. http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a6/