Geodesic
On existence of viscosity solutions for anisotropic parabolic equations with time-dependent exponents
Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 206-220

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In the present paper we consider the Cauchy—Dirichlet problem for anisotropic parabolic equation with gradient term which does not satisfy Bernstein—Nagumo condition. The existence and uniqueness of viscosity solution for this problem is proved. This solution is Hølder continuous in time and Lipschitz continuous in spatial variables.
Mots-clés : anisotropic parabolic equations
Keywords: viscosity solutions, time-dependent exponents. . 
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     author = {Ar. S. Tersenov},
     title = {On existence of viscosity solutions for anisotropic parabolic equations with time-dependent exponents},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {206--220},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a15/}
}
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Ar. S. Tersenov. On existence of viscosity solutions for anisotropic parabolic equations with time-dependent exponents. Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 206-220. http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a15/