| Abstract: |
| We study the lifespan of solutions to a discrete analogue of the semilinear heat equation with power nonlinearity, viewed as a discrete Fujita equation on the lattice. Previous work has shown that this model exhibits finite-time blow-up with the same Fujita critical exponent as in the continuous setting. We investigate how the lifespan depends on the size of small initial data and on the exponent relative to the Fujita critical exponent. We prove that, in both the subcritical and critical cases, the lifespan has the same order as that of the corresponding continuous problem. |
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