Work

Blow-up and global solutions for subcritical and critical parabolic equations in ${\mathbb R}^N$

Year: 2024

Type: article

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.

Source: Advances in Differential Equations

DOI: 10.57262/ade030-0304-141

Authors: Michinori Ishiwata, Bernhard Ruf, Federica Sani, Elide Terraneo

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4404775758

FWCI: 0.781

Cites:

Cited by: 1

Related to: 10