| Abstract: |
| This talk investigates the quenching phenomenon for numerical solutions of nonlinear heat equations incorporating non-local terms. Quenching occurs when a solution remains bounded while its time derivative blows up in finite time - a behavior well-documented in continuous parabolic models but increasingly complex in discrete settings.
We employ a finite-difference scheme to discretize the governing equations. A primary result of this work is the proof that discrete quenching always occurs whenever the continuous counterpart quenches. We also examine the convergence of the discrete quenching time to its continuous counterpart as the mesh size approaches zero. These results offer critical insights into the reliability of finite-difference methods for capturing singular behaviors in non-local nonlinear problems, ensuring that numerical artifacts do not obscure the underlying physical properties of the system. |
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