On Lipschitz solutions for some forward-backward parabolic equations. II: The case against Fourier
Seonghak Kim, Baisheng Yan
TL;DR
This paper investigates the existence and characteristics of Lipschitz solutions for certain forward-backward parabolic equations where the diffusion fluxes do not satisfy Fourier's inequality, extending previous work in the field.
Contribution
It provides new insights into solutions of forward-backward parabolic equations with non-Fourier fluxes, addressing cases previously unexplored.
Findings
Existence of Lipschitz solutions under non-Fourier flux conditions
Properties of solutions in the context of forward-backward parabolic equations
Extension of previous theoretical frameworks to new flux scenarios
Abstract
As a sequel to the paper [9], we study the existence and properties of Lipschitz solutions to the initial-boundary value problem of some forward-backward parabolic equations with diffusion fluxes violating Fourier's inequality.
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Taxonomy
TopicsNumerical methods in inverse problems · Advanced Mathematical Modeling in Engineering · Differential Equations and Boundary Problems