On the equipartition of energy for the critical NLW
Copyright policy )On the equipartition of energy for the critical NLW
The authors analyze some qualitative properties of a global solution to the Cauchy problem for the equation \(u_{tt}-\Delta u+\lambda u\left| u\right| ^{\frac{4}{n-2}}=0\) in both focusing and defocusing case, provided that such a global solution exists and satisfies the conservation of energy. They describe the asymptotic behavior of several energies as a consequence of a family of energy identities satisfied by the global solution of the above equation.
Asymptotic behavior of solutions to PDEs, Equipartition of energy, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Initial value problems for second-order hyperbolic equations, Nonlinear scattering, Critical NLW, Scattering theory for PDEs, nonlinear scattering, Morawetz estimate, dispersive estimate, Morawetz estimates, Dispersive estimates, family of energy identities, Analysis, Second-order nonlinear hyperbolic equations
Asymptotic behavior of solutions to PDEs, Equipartition of energy, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Initial value problems for second-order hyperbolic equations, Nonlinear scattering, Critical NLW, Scattering theory for PDEs, nonlinear scattering, Morawetz estimate, dispersive estimate, Morawetz estimates, Dispersive estimates, family of energy identities, Analysis, Second-order nonlinear hyperbolic equations
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