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Hyperbolic Equations and Characteristics
2000In Section 1.6, general second order equations were classified using characteristics, and this subject is revisited here. In the first chapter, the characteristics were used to classify the equations and to form a transformation to allow reduction to canonical form.
Gwynne A. Evans +2 more
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1933
The minimum equation. If A is a matrix of order n over a field p, the matrices I, A, A 2,..., A n 2 constitute n 2 + 1 sets of n 2 numbers each, and hence are linearly dependent in p. Thus A satisfies some equation $$m{\text{} }(\lambda){\text{} } = {\text{} }\lambda ^u {\text{} } + {\text{} }m_1 \lambda ^{u - 1} {\text{} } + {\text{} }...{\text{} }
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The minimum equation. If A is a matrix of order n over a field p, the matrices I, A, A 2,..., A n 2 constitute n 2 + 1 sets of n 2 numbers each, and hence are linearly dependent in p. Thus A satisfies some equation $$m{\text{} }(\lambda){\text{} } = {\text{} }\lambda ^u {\text{} } + {\text{} }m_1 \lambda ^{u - 1} {\text{} } + {\text{} }...{\text{} }
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Characteristic sets for ordinary differential equations
Programming and Computer Software, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marina V. Kondratieva, A. I. Ovchinnikov
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ON A METHOD OF SOLVING EQUATIONS WITH SIMPLE CHARACTERISTICS
Mathematics of the USSR-Sbornik, 1983This paper is devoted to the construction of k-differential equations for large values of the parameter k. The authors develop a method permitting one to construct solutions of such equations in the space Rn, with limiting absorption conditions. Together with the ideas of Legendre uniformization, the method allows one to construct solutions of boundary
Sternin, B. Yu., Shatalov, V. E.
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The bifurcation characteristics of the generalized Lorenz equations
Physica Scripta, 1996A graphical overview of the bifurcation characteristics of the generalized Lorenz equations obtained by Stenflo (1996 Physica Scripta 53 83) for nonlinear acoustic gravity waves in a rotational system is presented.
Yu, M.Y., Zhou, C.T., Lai, C.H.
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Differential equations in characteristic \(p\)
Compositio mathematica, 1995Let \(K\) be a differential field of characteristic \(p>0\). The aim of the paper is to classify differential equations over \(K\) and to develop Picard-Vessiot theory and differential Galois groups for these equations. It is supposed that \([K:K^p] = p\) and a choice of \(z\in K \backslash K^p\) is fixed.
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GENERALIZED CHARACTERISTICS AND THE HUNTER–SAXTON EQUATION
Journal of Hyperbolic Differential Equations, 2011The method of generalized characteristics yields an elementary proof of uniqueness of dissipative solutions to the Cauchy problem for the Hunter–Saxton equation.
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THE CHARACTERISTIC PROBLEM FOR THE EINSTEIN VACUUM EQUATIONS
Asymptotic Methods in Nonlinear Wave Phenomena, 2007We show how to prescribe the initial data of a characteristic problem satisfying the costraints, the smallness, the regularity and the asymptotic decay suitable to prove a global existence result. In this paper, the firstof two, we show in detail the construction of the initial data and give a sketch of the existence result.
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The Characteristic Equation and Stability
1977The local behavior of a system of differential equations $$fracd{X_i}dt = {f_i}\left( {{X_1},...,{X_n}} \right){\text{ }}\left( {i = 1,...,n} \right) $$ near an equilibrium point depends on the roots (eigenvalues) of the characteristic equation $$\left| {A - \lambda I} \right| = 0$$ (4.1) where A = (aij) is the matrix of first partial ...
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ON THE SOLUBILITY OF DIFFERENTIAL EQUATIONS WITH SIMPLE CHARACTERISTICS
Russian Mathematical Surveys, 1971This paper is a review of some recent results in the theory of solvability for general partial differential equations with \(C^\infty\) coefficients. Main results in this theory are due to H. Lewy, L. Hörmander, L. Nirenberg, F. Trèves and the author. Some examples are considered: Lewy's theorem, the oblique derivative problem for elliptic equations of
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