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Pré-Publication, Document De Travail Année : 2022

NEW LIFE-SPAN RESULTS FOR THE NONLINEAR HEAT EQUATION

Résumé

We obtain new estimates for the existence time of the maximal solutions to the nonlinear heat equation ∂tu − ∆u = |u| α u, α > 0 with initial values in Lebesgue, weighted Lebesgue spaces or measures. Non-regular, sign-changing, as well as non polynomial decaying initial data are considered. The proofs of the lower-bound estimates of lifespan are based on the local construction of solutions. The proofs of the upper-bounds exploit a well-known necessary condition for the existence of nonnegative solutions. In addition, we establish new results for lifespan using dilation methods and we give new lifespan estimates for Hardy-Hénon parabolic equations.
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Dates et versions

hal-03860535 , version 1 (18-11-2022)

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  • HAL Id : hal-03860535 , version 1

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Slim Tayachi, Fred B. Weissler. NEW LIFE-SPAN RESULTS FOR THE NONLINEAR HEAT EQUATION. 2022. ⟨hal-03860535⟩
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