Results 151 to 160 of about 11,284,175 (207)

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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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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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
semanticscholar   +1 more source

A Cauchy problem for the Cauchy–Riemann operator

Afrika Matematika, 2020
We study the Cauchy problem for a nonlinear elliptic equation with data on a piece $${\mathcal {S}}$$ of the boundary surface $$\partial {\mathcal {X}}$$ .
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The Cauchy-Stefan problem [PDF]

Acta Mechanica, 1982
The problem of solidification of two semi-infinite materials with arbitrarily prescribed initial conditions is studied. This is different from the classical Stefan problem; there are no prescribed boundary conditions. It is found that there are, depending on the prescribed initial conditions, four different possibilities: (i) solidification starts ...
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On the lateral Cauchy problem

Applied Mathematics and Computation, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On a characteristic Cauchy problem

Annali di Matematica Pura ed Applicata, 1987
The author considers the characteristic Cauchy problem (C) \[ u_{ts}+\sum^{n}_{j,k=1}a_{jk} u_{x_ jx_ k}+\sum^{n}_{j=1}b_ j u\quad_{x_ j}+cu=f\quad in\quad [0,T]\times {\mathbb{R}}\times {\mathbb{R}}\quad n, \] \[ u(0,s,x)=g(s,x),\quad (s,x)\in {\mathbb{R}}\times {\mathbb{R}}\quad n.
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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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Cauchy Problem

An Introduction to Mathematical Relativity, 2021
José Natário
semanticscholar   +1 more source

On the Nonlinear Cauchy Problem

2006
Our aim is to describe how to obtain, with the same procedure, several results of local existence, uniqueness and propagation of regularity for the solution of a quasilinear hyperbolic Cauchy Problem.
CICOGNANI, Massimo, ZANGHIRATI, Luisa
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