Resonant Nonlinear Geometric Optics for Weak Solutions of Conservation Laws
نویسندگان
چکیده
منابع مشابه
Validity of Nonlinear Geometric Optics for Entropy Solutions of Multidimensional Scalar Conservation Laws
Nonlinear geometric optics with various frequencies for entropy solutions only in L∞ of multidimensional scalar conservation laws is analyzed. A new approach to validate nonlinear geometric optics is developed via entropy dissipation through scaling, compactness, homogenization, and L–stability. New multidimensional features are recognized, especially including nonlinear propagations of oscilla...
متن کاملApproximate Solutions of Nonlinear Conservation Laws
This is a summary of ve lectures delivered at the CIME course on "Advanced Numerical Approximation of Nonlinear Hyperbolic Equations" held in Cetraro, Italy, on June 1997. Following the introductory lecture I | which provides a general overview of approximate solution to nonlinear conservation laws, the remaining lectures deal with the speciics of four complementing topics: Lecture II. Finite-d...
متن کاملError Estimates of Approximate Solutions for Nonlinear Scalar Conservation Laws
There has been an enormous amount of work on error estimates for approximate solutions to scalar conservation laws. The methods of analysis include matching the traveling wave solutions, [8, 24]; matching the Green function of the linearized problem [21]; weak W convergence theory [32]; the Kruzkov-functional method [19]; and the energy-like method [34]. The results on error estimates include: ...
متن کاملUniqueness of Weak Solutions to Systems of Conservation Laws
Consider a strictly hyperbolic nn system of conservation laws in one space dimension: u t + F(u) x = 0: () Relying on the existence of the Standard Riemann Semigroup generated by (), we establish the uniqueness of entropy-admissible weak solutions to the Cauchy problem, under a mild assumption on the variation of u along space-like segments.
متن کاملOn weak convergence of entropy solutions to scalar conservation laws
We prove that weak limits of entropy solutions to a one-dimensional scalar conservation law are entropy solutions as well. We consider a scalar conservation law ut + f(u)x = 0, (t, x) ∈ Π = (0, +∞)× R. (1) The flux function f(u) is supposed to be only continuous: f(u) ∈ C(R). Recall the notion of an entropy solution of (1) in the sense of Kruzhkov [6]. Definition 1. A bounded measurable functio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1994
ISSN: 0022-0396
DOI: 10.1006/jdeq.1994.1133