Sharp decay estimates for hyperbolic balance laws
نویسندگان
چکیده
منابع مشابه
Sharp L Stability Estimates for Hyperbolic Conservation Laws
Abstract. We introduce a generalization of Liu-Yang’s weighted norm to linear and to nonlinear hyperbolic equations. Following an approach due to the second author for piecewise constant solutions, we establish sharp L continuous dependence estimates for general solutions of bounded variation. Two different strategies are successfully investigated. On one hand, we justify passing to the limit i...
متن کاملDecay Estimates for Hyperbolic Systems
In this work we study the Sobolev spaces generated by pseudo-differential operators associated with the group of symmetry of general first order hyperbolic systems. In these spaces we establish pointwise estimates of the solutions of a class of first order systems having convex eigenvalues. Various physical models belong to this class. For example, we consider crystal optics systems and anisotr...
متن کاملLower compactness estimates for scalar balance laws
We study the compactness in Lloc of the semigroup (St)t≥0 of entropy weak solutions to strictly convex scalar conservation laws in one space dimension. The compactness of St for each t > 0 was established by P. D. Lax [1]. Upper estimates for the Kolmogorov’s ε-entropy of the image through St of bounded sets C in L ∩ L∞ which is denoted by Hε(St(C) | L(R)) := log2 Nε(St(C)). where Nε(St(C)) is ...
متن کاملAn Interesting Class of Hyperbolic Balance Laws
Abstract. This paper presents an observation that under reasonable conditions, many systems of hyperbolic balance laws from mathematical physics possess three structural properties. One of them can be understand as a variant of the celebrated Onsager reciprocal relation in Modern Thermodynamics. It displays a direct relation of irreversible processes to the entropy change. We show that the prop...
متن کاملOn a Class of Hyperbolic Balance Laws
Consider an n × n system of hyperbolic balance laws with coinciding shock and rarefaction curves. This note proves the well posedness in the large of this system, provided there exists a domain that is invariant both with respect to the homogeneous conservation law and to the ordinary differential system generated by the right hand side. No “non-resonance” hypothesis is assumed. 2000 Mathematic...
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: 2009
ISSN: 0022-0396
DOI: 10.1016/j.jde.2009.03.013