Global solutions for semilinear rough partial differential equations
Robert Hesse, Alexandra Neamtu
TL;DR
This paper develops a method to construct global solutions for semilinear parabolic rough PDEs using controlled rough path techniques, providing new a-priori estimates that avoid quadratic growth issues.
Contribution
It introduces a novel framework on Banach spaces for global solutions of semilinear rough PDEs, with estimates that circumvent quadratic terms.
Findings
Established global existence of solutions.
Derived new a-priori estimates free of quadratic terms.
Applicable to a broad class of semilinear rough PDEs.
Abstract
We construct global-in-time solutions for semilinear parabolic rough partial differential equations. We work on a scale of Banach spaces tailored to the controlled rough path approach and derive suitable a-priori estimates of the solution which do not contain quadratic terms.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Stability and Controllability of Differential Equations