Gevrey micro-regularity for solutions to first order nonlinear PDE
نویسندگان
چکیده
منابع مشابه
On microlocal analyticity of solutions of first-order nonlinear PDE
— We study the microlocal analyticity of solutions u of the nonlinear equation ut = f(x, t, u, ux) where f(x, t, ζ0, ζ) is complex-valued, real analytic in all its arguments and holomorphic in (ζ0, ζ). We show that if the function u is a C2 solution, σ ∈ CharLu and 1 i σ([Lu, Lu]) < 0 or if u is a C3 solution, σ ∈ CharLu, σ([Lu, Lu]) = 0, and σ([Lu, [Lu, Lu]]) 6= 0, then σ / ∈WFau. Here WFau de...
متن کاملPropagation of Gevrey Regularity for Solutions of Landau Equations
There are many papers concerning the propagation of regularity for the solution of the Boltzmann equation (cf. [5, 6, 8, 9, 13] and references therein). In these works, it has been shown that the Sobolev or Lebesgue regularity satisfied by the initial datum is propagated along the time variable. The solutions having the Gevrey regularity for a finite time have been constructed in [15] in which ...
متن کاملGeneralized Solutions to Nonlinear First Order Cauchy Problems
The recent significant enrichment, see [14] through [15], of the Order Completion Method for nonlinear systems of PDEs [12] resulted in the global existence of generalized solutions to a large class of such equations. In this paper we consider the existence and regularity of the generalized solutions to a family of nonlinear first order Cauchy problems. The spaces of generalized solutions are o...
متن کاملLoss of Gevrey Regularity for Asymptotic Optics
In this paper we will investigate some aspects of the asymptotic behavior of oscillatory integrals from the Gevrey point of view. We will give formal asymptotic expansions and study the Gevrey character of oscillatory integrals, in comparison with the Gevrey character of their amplitudes. We will deduce a formula for the loss of Gevrey regularity both for phase functions in the Morse class and ...
متن کاملAnti-periodic solutions for fully nonlinear first-order differential equations
In this paper, we study the anti-periodic boundary value problems for nonlinear first-order differential equations both in finite and in infinite dimensional spaces. Several new existence results are obtained. c © 2007 Elsevier Ltd. All rights reserved.
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.2009.06.021