{"title":"DIFFUSION WAVE INITIATION PROBLEM FOR A NONLINEAR PARABOLIC SYSTEM IN THE CASES OF SPHERICAL AND CYLINDRICAL SYMMETRY","authors":"A. L. Kazakov, L. F. Spevak","doi":"10.1134/S0021894424040102","DOIUrl":null,"url":null,"abstract":"<p>Solutions having the form of a diffusion wave propagating in a medium at rest with a finite velocity to a nonlinear parabolic reaction–diffusion system are constructed and studied. A problem of initiating a diffusion wave by boundary conditions specified on a sphere (circular cylindrical surface) is considered in the cases of spherical and cylindrical symmetry for the first time. An existence and uniqueness theorem for a solution in the class of analytical functions is proven. An exact solution is constructed in the form of explicit formulas. A step-by-step iterative algorithm based on the collocation method and expansion in radial basis functions is proposed. Numerical calculations are performed, and their results are verified using the exact solution.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"65 4","pages":"677 - 687"},"PeriodicalIF":0.5000,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mechanics and Technical Physics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0021894424040102","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
Solutions having the form of a diffusion wave propagating in a medium at rest with a finite velocity to a nonlinear parabolic reaction–diffusion system are constructed and studied. A problem of initiating a diffusion wave by boundary conditions specified on a sphere (circular cylindrical surface) is considered in the cases of spherical and cylindrical symmetry for the first time. An existence and uniqueness theorem for a solution in the class of analytical functions is proven. An exact solution is constructed in the form of explicit formulas. A step-by-step iterative algorithm based on the collocation method and expansion in radial basis functions is proposed. Numerical calculations are performed, and their results are verified using the exact solution.
期刊介绍：
Journal of Applied Mechanics and Technical Physics is a journal published in collaboration with the Siberian Branch of the Russian Academy of Sciences. The Journal presents papers on fluid mechanics and applied physics. Each issue contains valuable contributions on hypersonic flows; boundary layer theory; turbulence and hydrodynamic stability; free boundary flows; plasma physics; shock waves; explosives and detonation processes; combustion theory; multiphase flows; heat and mass transfer; composite materials and thermal properties of new materials, plasticity, creep, and failure.
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