Analysis and numerical simulation of a parabolic equation with non-local terms

Authors

  • Juan Pablo Límaco Institute of Computing, Federal University of Rio de Janeiro - RJ, Brazil.
  • Pitagoras P. de Carvalho Coord. de Matematica, Universidade Estadual do Piauí - UESPI, Teresina-PI, Brazil.
  • Mauro A. Rincon Institute of Computing, Federal University of Rio de Janeiro - RJ, Brazil.
  • Juan L. Ferrel Dep. de Matematica, Universidade Federal Fluminense, Niterói, RJ, Brazil.

DOI:

https://doi.org/10.17268/sel.mat.2025.02.02

Keywords:

Parabolic equations, Nonlocal nonlinearities, Well-posedness, Energy decay, Numerical Simulation

Abstract

In this work, we investigate the existence and uniqueness of global strong solutions, as well as the exponential decay of these solutions in bounded domains, for an initial-boundary value problem associated with parabolic equations involving nonlocal terms. The theoretical results are complemented by numerical simulations obtained using the finite element method for the spatial variable and the finite difference method for the temporal variable.

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Published

2025-12-27

How to Cite

Límaco, J. P., de Carvalho, P. P., Rincon, M. A., & Ferrel, J. L. (2025). Analysis and numerical simulation of a parabolic equation with non-local terms. Selecciones Matemáticas, 12(02), 273 - 287. https://doi.org/10.17268/sel.mat.2025.02.02

Issue

Vol. 12 No. 02 (2025): August - December

Section

Articles

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