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Top Academic Journal of Engineering and Mathematics
Vol. 6 No. 3 (2021): May-June
Articles

UNDERSTANDING QUENCHING BEHAVIOR IN SEMILINEAR EQUATIONS WITH A POTENTIAL

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  • Dr. Kouakou R. Koffi
Dr. Kouakou R. Koffi
Université Nangui Abrogoua, UFR-SFA, Laboratoire de Mathématiques et Informatique, 02 BP 801 Abidjan 02, Côte d’Ivoire

Published 2023-09-14

Keywords

  • initial-boundary value problem,
  • quenching,
  • , global existence,
  • partial differential equation,
  • potential function.

How to Cite

Kouakou , R. K. (2023). UNDERSTANDING QUENCHING BEHAVIOR IN SEMILINEAR EQUATIONS WITH A POTENTIAL. Top Academic Journal of Engineering and Mathematics, 6(3), 40–50. Retrieved from https://topjournals.org/index.php/TAJEM/article/view/386

Copyright (c) 2023 Top Academic Journal of Engineering and Mathematics

Creative Commons License

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Abstract

Abstract: This study investigates an initial-boundary value problem in a bounded domain Ω with a smooth boundary ∂Ω. The problem involves a partial differential equation with a nonnegative locally Hölder continuous potential ????(????,????). We aim to understand the behavior of the solution ????(????,????) over a given time interval (0, T), where T can be finite or infinite. A solution to this problem is defined as a function ????(????,????) that is continuous in Ω×(0,????), twice continuously differentiable in ????, and once in ????. In cases where T is finite, the solution ???? exhibits quenching behavior, where it converges to zero as time approaches T. The time T at which this quenching occurs is referred to as the quenching time. In contrast, if T is infinite, the solution is said to exist globally, indicating its persistence over an indefinite time interval. This investigation delves into the dynamics of solutions to shed light on the phenomena of quenching and global existence, providing insights into the behavior of the system in response to the given initial-boundary conditions and the influence of the potential ????(????,????)

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