Coefficients with unbounded derivatives in hyperbolic equations
Copyright policy )Coefficients with unbounded derivatives in hyperbolic equations
AbstractWe are concerned with the problem of determining the sharp regularity of the coefficients with respect to the time variable t in order to have a well‐posed Cauchy problem in H∞ or in Gevrey classes for linear or quasilinear hyperbolic operators of higher order. We use and mix two different scales of regularity of global and local type: the modulus of Hölder continuity and/or the behaviour with respect to |t − t1|−q, q ≥ 1, of the first derivative as t tends to a point t1. Both are ways to weaken the Lipschitz regularity. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
sharp regularity of the coefficients, \(H^\infty\) well-posedness, Initial value problems for higher-order hyperbolic equations, General existence and uniqueness theorems (PDE), Gevrey well-posedness, non-regular coefficients, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, quasilinear hyperbolic operators of higher order
sharp regularity of the coefficients, \(H^\infty\) well-posedness, Initial value problems for higher-order hyperbolic equations, General existence and uniqueness theorems (PDE), Gevrey well-posedness, non-regular coefficients, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, quasilinear hyperbolic operators of higher order
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