Bilateral Estimates of Solutions with Blow up Regime of the Nonlinear Heat Equation with a Quadratic Source
DOI:
https://doi.org/10.52575/2687-0959-2023-55-3-273-284Keywords:
Approximation of Solutions, Compact Support, Nonlinear Equation of Heat Transfer, Blow-up Regime, Etalon SolutionAbstract
Solutions u(x, t) ≥ 0, x ∈ R, t ≥ 0 with compact support of one-dimensional quasilinear heat transfer equation
degenerated at u(x, t) = 0 is studied. The equation has the linear on u transport coefficient and self-consistent source αu + βu2 of general type. Bulateral estimates of the blow-up time for solutions with a compact support are established, functionally depended on the initial conditions u(x, t).
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