Nonlinear Wave EquationsCRC Press, 5 sep 1995 - 296 pagina's This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods. |
Inhoudsopgave
Preface | 1 |
Notes | 40 |
Local and Global Existence | 47 |
Singularity Formation | 87 |
Solitons and Inverse Scattering | 135 |
Perturbation Methods | 189 |
General Relativity | 219 |
| 273 | |
Overige edities - Alles bekijken
Veelvoorkomende woorden en zinsdelen
Algebra analytic Appl applications assume asymptotic blow-up surface bounded Cauchy data Cauchy problem characteristic coefficients Comm compute conservation law consider constant constraint coordinates curvature decay defined derivatives ds² eigenfunctions eigenvalues Einstein's equations equa estimate evolution equation example expansion exponential finite follows formal formula Fourier transform geodesic given global existence hyperbolic equations hypersurface infinity initial-value problem integral invariant inverse scattering iteration KdV equation Kichenassamy Klainerman Klein-Gordon equation Lax pair linear Math method metric Minkowski space Nash-Moser Nash-Moser theorem nonlinear wave nonlinear wave equations norm Note null condition obtain operator parameter perturbation proof propagation properties prove regularity satisfy Schrödinger equation Show singularity formation Sobolev inequality Sobolev spaces solitons solve spacetime symmetric tensor theorem theory three space dimensions timelike tions u₁ vanishes variables vector wave equation zero
Populaire passages
Pagina 269 - H. Friedrich. On the existence of n-geodesically complete or future complete solutions of Einstein's equations with smooth asymptotic structure.