Asymptotics for Dissipative Nonlinear Equations
Hayashi, Nakao.
Asymptotics for Dissipative Nonlinear Equations [electronic resource] / by Nakao Hayashi, Pavel I. Naumkin, Elena I. Kaikina, Ilya A. Shishmarev. - XI, 557 p. online resource. - Lecture Notes in Mathematics, 1884 0075-8434 ; . - Lecture Notes in Mathematics, 1884 .
Preliminary results -- Weak Nonlinearity -- Critical Nonconvective Equations -- Critical Convective Equations -- Subcritical Nonconvective Equations -- Subcritical Convective Equations.
Many 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.
9783540320609
10.1007/b133345 doi
Global analysis (Mathematics).
Differential equations, partial.
Integral equations.
Analysis.
Partial Differential Equations.
Integral Equations.
Theoretical, Mathematical and Computational Physics.
QA299.6-433
515
Asymptotics for Dissipative Nonlinear Equations [electronic resource] / by Nakao Hayashi, Pavel I. Naumkin, Elena I. Kaikina, Ilya A. Shishmarev. - XI, 557 p. online resource. - Lecture Notes in Mathematics, 1884 0075-8434 ; . - Lecture Notes in Mathematics, 1884 .
Preliminary results -- Weak Nonlinearity -- Critical Nonconvective Equations -- Critical Convective Equations -- Subcritical Nonconvective Equations -- Subcritical Convective Equations.
Many 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.
9783540320609
10.1007/b133345 doi
Global analysis (Mathematics).
Differential equations, partial.
Integral equations.
Analysis.
Partial Differential Equations.
Integral Equations.
Theoretical, Mathematical and Computational Physics.
QA299.6-433
515