Multiscale functions, scale dynamics, and applications to partial differential equations

DOI10.1063/1.4948745zbMath1338.00042arXiv1509.01048OpenAlexW3098843761MaRDI QIDQ2814225

Frédéric Pierret, Jacky Cresson

Publication date: 20 June 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.01048

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) General applied mathematics (00A69) General theory of mathematical modeling (00A71) Physics (00A79) Dimension theory of smooth dynamical systems (37C45) Foundations of fluid mechanics (76A02) Axiomatics, foundations (70A05) Dynamic equations on time scales or measure chains (34N05)

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Cites Work

• Time scale differential, integral, and variational embeddings of Lagrangian systems
• Non-differentiable variational principles
• Non-differentiable embedding of Lagrangian systems and partial differential equations
• Analysis on measure chains - a unified approach to continuous and discrete calculus
• A remark on continuous, nowhere differentiable functions
• On the critical case of Okamoto's continuous non-differentiable functions
• Global bifurcations and chaos. Analytical methods
• The local Hölder function of a continuous function
• NON-DIFFERENTIABLE DEFORMATIONS OF ℝⁿ
• Stochastic embedding of dynamical systems
• Scale calculus and the Schrödinger equation
• Stochastic differential equations. An introduction with applications.
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