Real eternal PDE solutions are not complex entire: a quadratic parabolic example

2024/03/11 by Fiedler, Bernold, Stuke, Hannes
#35B08 #35B34 #35B44 #35K58 #37F44 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.06490

Abstract

In parabolic or hyperbolic PDEs, solutions which remain uniformly bounded for all real times t=r∈ℝ are often called PDE entire or eternal. For example, consider the quadratic parabolic PDE w_t=w_xx+6w²-λ, for 00, and are currently limited to unstable dimensions n≤22, or to fast unstable manifolds of dimensions d<1+\tfrac1√(2)n.

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