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Group classification and analytical solutions of a radially symmetric avascular cancer model
Author(s) -
Bortuli Altemir,
Freire Igor Leite,
Maidaorberto Anibal
Publication year - 2021
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12416
Subject(s) - homogeneous space , invariant (physics) , partial differential equation , group (periodic table) , mathematics , symmetry group , differential equation , symmetry (geometry) , mathematical analysis , mathematical physics , pure mathematics , physics , geometry , quantum mechanics
Abstract We consider a system of partial differential equations modeling tumors. The system under consideration describes the spatial dynamics of the tumor cells, extracellular matrix, and matrix degrading enzymes. We first carry out a complete group classification of the Lie point symmetries of this model. Next, we use symmetry techniques to construct invariant solutions for it. In addition, we consider a second system of partial differential equations, coupling to the original one the concentration of oxygen, and we find several analytical solutions to this system. Most of the solutions are biologically relevant and consistent with the evolution of such tumors.