We study the local well-posedness in the framework of the Sobolev space (Formula presented), 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.
Blow-up and global solutions for subcritical and critical parabolic equations in {$\Bbb R^N$} / M. Ishiwata, B. Ruf, F. Sani, E. Terraneo. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - 30:3-4(2025 Apr), pp. 141-176. [10.57262/ade030-0304-141]
Blow-up and global solutions for subcritical and critical parabolic equations in {$\Bbb R^N$}
E. TerraneoUltimo
2025
Abstract
We study the local well-posedness in the framework of the Sobolev space (Formula presented), 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.
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