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The Third‐Order Nonlinear Evolution Equation Governing Wave Propagation in Relaxing Media
Author(s) -
Varlamov Vladimir V.
Publication year - 1997
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 - 10.1111/1467-9590.00055
Subject(s) - uniqueness , mathematical analysis , isotropy , nonlinear system , mathematics , initial value problem , space (punctuation) , representation (politics) , series (stratigraphy) , evolution equation , wave equation , physics , optics , computer science , quantum mechanics , paleontology , politics , law , political science , biology , operating system
Initial value problem for the third‐order nonlinear evolution equation governing wave propagation in relaxing media is considered for the case of two space dimensions and small initial data. Existence and uniqueness of the classical solution is established and the solution itself is constructed in the form of a series in the small parameter present in the initial conditions. Long time asymptotic representation is found, which shows that the nonlinearity does not contribute to its major term. The latter consists of two parts corresponding to isotropic and nonisotropic transfer of small perturbations in space.