Abstract
We study the local well-posedness in the framework of the Sobolev space $H^1(\mathbb R^N)$, $N \geq 3$, for a semilinear parabolic equation with asymptotically polynomial nonlinearity up to the critical Sobolev growth. Then we establish the dichotomy between blow-up and global existence for solutions with small energy by means of variational methods and the so-called potential well argument.
Citation
Michinori Ishiwata. Bernhard Ruf. Federica Sani. Elide Terraneo. "Blow-up and global solutions for subcritical and critical parabolic equations in ${\mathbb R}^N$." Adv. Differential Equations 30 (3/4) 141 - 176, Marh/April 2025. https://doi.org/10.57262/ade030-0304-141
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