Comparison theorem in blow-up problems for reaction diffusion equations and for their approximations
https://doi.org/10.29235/1561-8323-2023-67-5-366-372
Abstract
In this paper, blow-up sufficient conditions and upper bound of blow-up time for solution of Neumann and Dirichlet problems for reaction diffusion equations with non-linear gradient have been obtained. These equations have been found from the comparison of theorems, Jensen’s inequality and conservations laws. By using a similar proof approach for the finite-difference case, the finite-difference scheme was constructed, approximating the above-mentioned Neumann problem, for which sufficient conditions and upper bound of blow-up time, consistent with appropriate conditions and bound for the appropriate differential problem, have been obtained.
About the Author
D. A. Schadinskii
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Denis A. Schadinskii, Junior Researcher, Master (Physics and Mathematics)
220072
11, Surganov Str.
Minsk
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