Vol. 1 No. 09 (2025), Articles
Vol. 1 No. 09 (2025)

BLOW-UP SOLUTIONS FOR A CLASS OF NONLINEAR PARABOLIC EQUATIONS NON-DIVERGENCE FORM

Articles
Published 21-11-2025
  • Matyakubov Alisher Samandarovich
  • Raupov Dilmurod Rasulovich
  • Nortillayev Komil Davlatilievich
Matyakubov Alisher Samandarovich
Raupov Dilmurod Rasulovich
Nortillayev Komil Davlatilievich
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Keywords

matematical model, asymptotic, combustion, nonlinear parabolic equation, self-similar solution, non-divergent form, Blow-up properties of solutions, global solutions.

How to Cite

Alisher Samandarovich , M., Dilmurod Rasulovich , R., & Komil Davlatilievich, N. (2025). BLOW-UP SOLUTIONS FOR A CLASS OF NONLINEAR PARABOLIC EQUATIONS NON-DIVERGENCE FORM . Advances in Science and Education, 1(09), 99-102. https://doi.org/10.70728/edu.v01.i09.023
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Abstract

In this article, nonlinear equations of non-divergent parabolic type are considered. Solutions of nonlinear equations of non-divergent parabolic type with Blow-up properties under boundary conditions were also investigated. Hopf's maximum principle was used in the evaluation of the solutions. For nonlinear equations of non-divergent parabolic type, the conditions for the global existence of solutions over time and the existence of unbounded (blow-up) solutions are obtained. Top estimates of blow-up and global solutions of nonlinear equations of non-divergent parabolic type are shown. The properties of Blow-up solutions of a nonlinear parabolic equation of non-divergent form under boundary conditions were investigated, and estimates for explosion times were obtained in the problems of heat diffusion and combustion processes. In mathematical models describing the processes of heat diffusion and combustion in nonlinear media, the power of the source (absorption) is also common.

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References

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