Asymptotics for Dissipative Nonlinear EquationsMany of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others. |
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asymptotic behavior behavior of solutions Burgers Cauchy problem contraction mapping damped wave decay estimate define Denote estimate of Lemma exists a unique function Green operator Hayashi heat equation Hence Hölder inequality initial data uo integral equation integrating with respect ISSN Korteweg-de Vries-Burgers equation L¹,a L¹‚ª large time asymptotic linear operator nonlinear heat equation norm obtain operator G operator L satisfy optimal time decay proof of Theorem prove right-hand side self-similar Sobolev space subcritical sufficiently small sup sup Suppose T₁ type equations u₁ uniformly with respect unique global solution unique solution valid virtue Young inequality ησ