An existence result for a general non-linear parabolic equation and related eigenvalue problem through a standard variational approach

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This paper studies the existence of solutions for a general nonlinear parabolic partial differential equation and a related eigenvalue problem using a variational approach linked to a time-discretized model. The authors establish that a solution exists at each instant of time in the discretized framework. The communication is brief and explicitly presented as a preprint, with preliminary information and no peer review, and the summary provided does not detail specific mathematical conditions or results beyond the existence claim. The paper does not explicitly discuss endometriosis or adenomyosis; it was included in the corpus via a keyword match in the upstream search index.

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Abstract

This short communication develops an existence result for a general non-linear parabolic equation and related eigenvalue problem. The method of proof comprises a variational approach for establishing a concerning solution existence at each instant of time, related to a model discretized in time. Supplementary Material File (parabolic-january-2025-10.pdf) - Download - 197.41 KB Information & Authors Information Version history Copyright This work is licensed under a Non Exclusive No Reuse License.

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Authors Metrics & Citations Metrics Article Usage 260views 113downloads Citations Download citation Fabio Botelho, Fabio Silva Botelho. An existence result for a general non-linear parabolic equation and related eigenvalue problem through a standard variational approach. Authorea. 29 January 2025. DOI: https://doi.org/10.22541/au.173819108.88986539/v1 DOI: https://doi.org/10.22541/au.173819108.88986539/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.

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last seen: 2026-05-20T01:45:00.602351+00:00