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Asymptotic Behavior of Solutions to Nonlinear Equations with Dissipation for Large x and t
Author(s) -
Naumkin P. I.
Publication year - 1992
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 - 10.1002/sapm199287145
Subject(s) - dissipation , generalization , nonlinear system , mathematics , initial value problem , mathematical analysis , cauchy problem , character (mathematics) , class (philosophy) , dissipative system , mathematical physics , physics , geometry , thermodynamics , quantum mechanics , computer science , artificial intelligence
In this paper we continue to study large time asymptotic behavior of solutions to the Cauchy problem for a class of nonlinear nonlocal equations with dissipation. When t → ∞ and x → ∞ simultaneously, the asymptotics of solutions for a generalization of the Kolmogorov‐Petrovsky‐Piscounov equation, a model equation studied by Whitham, and an equation introduced by Ott, Sudan, and Ostrovsky is found. The character of asymptotics obtained is quasilinear.