Geodesic
Blow-up in difference schemes that approximate Neumann problems for nonlinear parabolic equations
Trudy Instituta matematiki, Tome 32 (2024) no. 2, pp. 43-55

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In this paper, based on the discrete analogue of comparison theorems and Jensen's inequality, blow-up conditions and upper bound of blow-up time of the solution of implicit finite-different problem which approximates Neumann problems for various nonlinear parabolic equations are obtained. Blow-up conditions and upper bound of blow-up time of approximated differential problems are given, which are obtained and based on comparison theorems and Jensen's inequality.
Keywords: comparison theorems, blow-up, discrete analogue of comparison theorems, nonlinear parabolic equations. 
@article{TIMB_2024_32_2_a3,
     author = {D. A. Schadinskii},
     title = {Blow-up in difference schemes that approximate {Neumann} problems for nonlinear parabolic equations},
     journal = {Trudy Instituta matematiki},
     pages = {43--55},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2024_32_2_a3/}
}
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D. A. Schadinskii. Blow-up in difference schemes that approximate Neumann problems for nonlinear parabolic equations. Trudy Instituta matematiki, Tome 32 (2024) no. 2, pp. 43-55. http://geodesic.mathdoc.fr/item/TIMB_2024_32_2_a3/