منابع مشابه
Nonlinear Wave Equations
where := −∂2 t +∆ and u[0] := (u, ut)|t=0. The equation is semi-linear if F is a function only of u, (i.e. F = F (u)), and quasi-linear if F is also a function of the derivatives of u (i.e. F = F (u,Du), where D := (∂t,∇)). The goal is to use energy methods to prove local well-posedness for quasilinear equations with data (f, g) ∈ Hs × Hs−1 for large enough s, and then to derive Strichartz esti...
متن کاملNonlinear Wave Equations
This paper explores the properties of nonlinear wave equations. The proof for the existence and uniqueness of solutions to the 1+1 dimensional linear wave equation with smooth data is given. The D’Alembert formula is then presented in its full generality for the nonlinear equation. Important properties like the domain of dependence and propagation of information are discussed and motivated. The...
متن کاملNonlinear stochastic wave equations
In this paper we study the Cauchy problem for the semilinear stochastic wave equation (@ 2
متن کاملNonlinear Wave Equations
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions, useful in the analysis of semilinear equations, and next to the study of nonlinear wave interactions, arising in fully nonlinear equations. The dispersion phe...
متن کاملMath 279: Nonlinear Wave Equations
These are notes in progress a graduate course in mathematics. Any suggestions or comments are welcome and can be sent to [email protected].
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1992
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1992-00278-1