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The Cauchy problem is severely ill-posed, and a general mollification method is introduced to solve the problem. Both the a priori and a posteriori choice strategies of the regularization parameter are proposed, and error estimations of the corresponding regularization solutions are also presented. Finally, two numerical examples are introduced to show the effectiveness of the general mollification regularization method.<\/jats:p>","DOI":"10.3390\/sym16111549","type":"journal-article","created":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T06:06:54Z","timestamp":1731996414000},"page":"1549","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A General Mollification Regularization Method to Solve a Cauchy Problem for the Multi-Dimensional Modified Helmholtz Equation"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1628-3028","authenticated-orcid":false,"given":"Huilin","family":"Xu","sequence":"first","affiliation":[{"name":"College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baoxia","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Duanmei","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1016\/j.apm.2012.03.014","article-title":"Some remarks on a modified Helmholtz equation with inhomogeneous source","volume":"37","author":"Nguyen","year":"2013","journal-title":"Appl. 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