in [Chicago] .
Written in English
|The Physical Object|
|Number of Pages||151|
Fourier integral operators with complex-valued phase function and the Cauchy problem for hyperbolic operators.- The effectively hyperbolic Cauchy problem. Series Title: Lecture notes in mathematics (Springer-Verlag), Responsibility: Kunihiko Kajitani, Tatsuo Nishitani. More information: Inhaltstext. The correctness of the Cauchy problem in the Gevrey classes for operators with hyperbolic principal part is shown in the first part. In the second part, the correctness of the Cauchy problem for effectively hyperbolic operators is proved with a precise estimate of the loss of derivatives. This method can be applied to other (non) hyperbolic. In this paper we deal with the Cauchy problem for hyperbolic equations with co-efﬁcients of polynomial growth in the space variables. A pio neering work on this topic is the book by Cordes , where strictly hyperbolic equations are considered. The au-thor proves well posedness for the related Cauchy problem in S(R n), S 0 (n) and in the. The Cauchy problem for hyperbolic functional differential equations is considered. Volterra and Fredholm dependence are considered. A theorem on the local existence of generalized solutions.
Gramchev T., Ruzhansky M. () Cauchy Problem for Some 2 × 2 Hyperbolic Systems of Pseudo-differential Equations with Nondiagonalisable Principal Part. In: Cicognani M., Colombini F., Del Santo D. (eds) Studies in Phase Space Analysis with Applications to PDEs. Progress in Nonlinear Differential Equations and Their Applications, vol Akisato Kubo, Michael Reissig, Construction of Parametrix to Strictly Hyperbolic Cauchy Problems with Fast Oscillations in NonLipschitz Coefficients†, Communications in Partial Differential Equations, /PDE, 28, , (), (). Lectures on Cauchy Problem By Sigeru Mizohata Notes by M.K. Venkatesha Murthy and B.V. Singbal No part of this book may be reproduced in any form by print, microﬁlm or any other means with-out written permission from the Tata Institute of 3 Cauchy problem for a single equation . Browse other questions tagged partial-differential-equations bessel-functions wave-equation riemann-integration hyperbolic-equations or ask your own question. Featured on Meta A big thank you, Tim Post.
The hyperbolic equation is very important in view of its applications, moreover many important mathematical concepts are related to the problems on hyperbolic equations. The hyperbolic equation could be characterized by the properties, which are as follows: (1) it has the property of finite propagation speed; (2) it is C ∞ -wellposed not only. For noneffectively hyperbolic operators, it was proved in the late of s that for the Cauchy problem to be C ∞ well posed the subprincipal symbol has to be real and bounded, in modulus, by the sum of modulus of pure imaginary eigenvalues of the Hamilton map. This chapter discusses the Cauchy problem for uniformly diagonalizable hyperbolic systems of linear partial differential equations in Gevrey classes. It also discusses the Cauchy problem for uniformly diagonalizable hyperbolic systems whose coefficients are in Gevrey class. Topics include the general properties of Cauchy's problem, the fundamental formula and the elementary solution, equations with an odd number of independent variables, and equations .