Results 291 to 300 of about 11,623,619 (358)

On the Cauchy Problem for Integro-Differential Equations in the Scale of Spaces of Generalized Smoothness

, 2017
Parabolic integro-differential model Cauchy problem is considered in the scale of Lp -spaces of functions whose regularity is defined by a scalable Levy measure. Existence and uniqueness of a solution is proved by deriving apriori estimates.
R. Mikulevičius, C. Phonsom
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A Cauchy problem for the Cauchy–Riemann operator

Afrika Matematika, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Henkin G.M., Shananin A.A.
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The Cauchy Problem

1997
Suppose L 1 and L 2 are topological vector spaces and T : L 1 → L 2 is a continuous linear mapping. We consider the aspect of Problem 7.1.1 connected with describing the range of the mapping T.
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On the Cauchy Problem for Axi-Symmetric Vortex Rings

, 2013
We consider the classical Cauchy problem for the three dimensional Navier–Stokes equation with the initial vorticity ω0 concentrated on a circle, or more generally, a linear combination of such data for circles with common axis of symmetry.
Hao Feng, V. Sverák
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