Results 201 to 210 of about 9,053 (252)

The Cauchy Problem

1991
The contemporary state of the question for the correctness of the Cauchy problem is exposed for differential and pseudo-differential operators with non-homogeneous symbols. Ch.1,2 are devoted to constant coefficients, criteria for the correctness of the Cauchy problem in spaces of functions and distributions of power and exponential decrease and ...
Volevich, L. R., Gindikin, S. G.
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The Cauchy Problem

1984
This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations.
Hector O. Fattorini, Adalbert Kerber
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A Cauchy problem for the Cauchy–Riemann operator

Afrika Matematika, 2020
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The Cauchy Problem

2009
The theory of the Cauchy problem for hyperbolic conservation laws is confronted with two major challenges. First, classical solutions, starting out from smooth initial values, spontaneously develop discontinuities; hence, in general, only weak solutions may exist in the large. Next, weak solutions to the Cauchy problem fail to be unique.
Li Tatsien, Wang Libin
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Some singular cauchy problems

Annali di Matematica Pura ed Applicata, 1961
Existence and uniqueness theorems for some generalizedEuler-Poisson-Darboux equations are proved and growth and convexity properties of the solutions are studied for multiply subharmonic initial values.
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The Cauchy problem

1995
In Theorem 2.1.10 we saw that if A is the infinitesimal generator of a C0-semigroup T(t), the solution of the abstract homogeneous Cauchy initial value problem $$\begin{array}{*{20}{c}}{\dot z\left( t \right) = Az\left( t \right),}&{t \geqslant 0,}&{z\left( 0 \right) = {z_0} \in D\left( A \right)}\end{array}$$ is given by $$z\left( t \right)
Ruth F. Curtain, Hans Zwart
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Cauchy’s Problem

1970
Cauchy’s problem with holomorphic data can be studied at the characteristic points of the hypersurface S carrying Cauchy’s data; (for linear equations, see [4], which improves [3; I]; for non linear equations, see Y. Choquet-Bruhat [1]). In general its solution u is algebroid at those points (but an equation with constant coefficients and constant data
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On the Degenerate Cauchy Problem

Canadian Journal of Mathematics, 1965
The problem treated here is an abstract version of the Cauchy problem for an equation of mixed type in the hyperbolic region with initial data on the parabolic line (cf. 2, 3, 5, 11, 13, 14, 15, 16, 21, 27). A more complete bibliography may be found in (3, 5, 18). We begin with the equation (6)(1.1)
Carroll, Robert W., Wang, C. L.
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Computation for MultiDimensional Cauchy Problem

SIAM Journal on Control and Optimization, 2003
The authors deal with a regularization method in order to solve numerically the classical Cauchy problem for the Laplace equation. They prove the convergence and the stability of the method even when the Cauchy data have noises. A numerical example in the three-dimensional case is carried out.
Wei, T., Hon, Y. C., Cheng, J.
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On the Cauchy–Gelfand problem

Doklady Mathematics, 2015
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Henkin G.M., Shananin A.A.
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