Work

Rigorous C1 integration of dissipative PDEs

Year: 2026

Type: article

Abstract: We introduce a new $C^1$ algorithm for the rigorous integration of dissipative partial differential equations. The algorithm is designed for computer-assisted proofs that require rigorous control of both solutions and their derivatives with respect to initial data. As applications, we establish the existence of locally attracting periodic orbits for initial and boundary value problems for two non-autonomous dissipative PDEs: the Chafee-Infante equation and the Burgers equation with a fractional Laplacian.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2026.114831

Author: Jakub Banaśkiewicz

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

OpenAlex ID: W7148509138

FWCI:

Cites: 13

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