What question did this study set out to answer?

This work aims to establish a rigorous axiomatic framework for discrete variable lattice dissipative functionals and prove the well-posedness of the Helmholtz problem.

August 13, 2026Open Access

Axiomatic System and Core Constants of Discrete Variable Lattice Dissipative Functionals Well-Posedness Proof of Discrete Dissipative Helmholtz Problem on Finite Hierarchical Fractal Lattice

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ZLZhongqiang Liu

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Implication

This theoretical framework proves well-posedness in discrete mathematical systems, implying robust solutions for energy transport models.

Key Points

This work aims to establish a rigorous axiomatic framework for discrete variable lattice dissipative functionals and prove the well-posedness of the Helmholtz problem.
Constructed an axiomatic system using four independent axioms as the basis.
Defined gradient, divergence, and curl in a three-dimensional discrete lattice space.
Used the Lax-Milgram theorem to demonstrate the existence, uniqueness, and stability of the discrete Helmholtz boundary value problem.
Proven second-order uniform convergence of discrete operators to continuous differential operators.
Established a discrete Gauss-Stokes integral identity to support the discrete-continuous mapping operator.
Showed that a steady-state scale parameter corresponds uniquely to the golden ratio.

Cite This Study

Zhongqiang Liu (2026) studied this question.

synapsesocial.com/papers/6a7d76652b0e0cff3f63fa52 https://doi.org/10.5281/zenodo.21890020

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Axiomatic System and Core Constants of Discrete Variable Lattice Dissipative Functionals Well-Posedness Proof of Discrete Dissipative Helmholtz Problem on Finite Hierarchical Fractal Lattice

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Cite This Study

Axiomatic System and Core Constants of Discrete Variable Lattice Dissipative Functionals Well-Posedness Proof of Discrete Dissipative Helmholtz Problem on Finite Hierarchical Fractal Lattice

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