Well-Posedness for the Reaction-Diffusion Equation with Temperature in a critical Besov Space

Chun Liu; Jan-Eric Sulzbach

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Well-Posedness for the Reaction-Diffusion Equation with Temperature in a critical Besov Space

Chun Liu, Jan-Eric Sulzbach

Analysis of PDEs · Submitted 25 Jan 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim From this we recover a linearized model for a system close to equilibrium and we analyze the global-in-time well-posedness of the system for small initial data for a critical Besov space.

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arXiv ID2101.10419 (version 2)

Pith IDCTFISFLA, Pith's permanent record of this paper and its review

CitationChun Liu, Jan-Eric Sulzbach. "Well-Posedness for the Reaction-Diffusion Equation with Temperature in a critical Besov Space." arXiv:2101.10419 (2021). https://pith.science/paper/CTFISFLA

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We derive a model for the non-isothermal reaction-diffusion equation. Combining ideas from non-equilibrium thermodynamics with the energetic variational approach we obtain a general system modeling the evolution of a non-isothermal chemical reaction with general mass kinetics. From this we recover a linearized model for a system close to equilibrium and we analyze the global-in-time well-posedness of the system for small initial data for a critical Besov space.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We derive a model for the non-isothermal reaction-diffusion equation.	contribution 0.91	0.93	0.05	asserted 1.00
s1	Combining ideas from non-equilibrium thermodynamics with the energetic variational approach we obtain a general system modeling the evolution of a non-isothermal chemical reaction with general mass kinetics.	method 0.72	0.91	0.07	asserted 1.00
s2	From this we recover a linearized model for a system close to equilibrium and we analyze the global-in-time well-posedness of the system for small initial data for a critical Besov space.	result 0.52	0.94	0.81	asserted 1.00

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Original abstract

We derive a model for the non-isothermal reaction-diffusion equation. Combining ideas from non-equilibrium thermodynamics with the energetic variational approach we obtain a general system modeling the evolution of a non-isothermal chemical reaction with general mass kinetics. From this we recover a linearized model for a system close to equilibrium and we analyze the global-in-time well-posedness of the system for small initial data for a critical Besov space.

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Finally, we want to remark that for a similar system of equations with only Darcy-type dissipation we are able to show the well-posedness of the system in a critical Besov space [ref] .

The Brinkman-Fourier System with Ideal Gas Equilibrium · Conclusion and Remarks · 0.88

Cites it as background 2 papers

Most recent results were obtained by [ref] and [ref] deriving better a priori bounds and showing positivity for the absolute temperature and by [ref] , where the well-posed of a non-isothermal reaction-diffusion sytem in a critical Besov space is shown.

The Brinkman-Fourier System with Ideal Gas Equilibrium · Introduction · 0.91
The last but not the least important issue is with the numerical simulation viewpoint, which is very useful in studying the patterns and stability/instability problems, and some coupling effects with other different mechanics such as temperature and electric fields [ref] .

On a Reversible Gray-Scott Type System from Energetic Variational Approach and Its Irreversible Limit · Conclusion · 0.90

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