A note on lifespan estimates for higher-order parabolic equations

2025/12/04 by Tobakhanov, Nurdaulet N., Torebek, Berikbol T.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.04428

Abstract

We investigate the lifespan of solutions to the higher-order semilinear parabolic equation u_t+(-Δ)^m u=|u|^p, x ∈ ℝⁿ, tgt;0 with initial data. We focus on the precise asymptotic behavior of the lifespan of nontrivial solutions. By combining the test function method and semigroup estimates, we derive both upper and lower bounds for the lifespan of solutions T_ε ≃ \\beginarraylε^-((1)/(p-1)-(n)/(2m))^-1, 1

Citations

• On the critical behavior for the semilinear biharmonic heat equation with forcing term in an exterior domain
• New life-span results for the nonlinear heat equation
• Blow-up rates for higher-order semilinear parabolic equations with\n nonlinear memory term
• Existence of solutions for a higher-order semilinear parabolic equation with singular initial data
• Construction of type I blowup solutions for a higher order semilinear\n parabolic equation
• Local well-posedness and global existence for the biharmonic heat\n equation with exponential nonlinearity

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