Perturbations of skew-Hermitian bundles and the degenerate cauchy problem

1989 ◽  
Vol 41 (8) ◽  
pp. 931-935 ◽  
Author(s):  
A. G. Rutkas
Keyword(s):  
Cauchy Problem ◽  
Degenerate Cauchy Problem

scholarly journals Existence for a degenerate Cauchy problem

2008 ◽  
Vol 128 (2) ◽  
pp. 213-249 ◽  
Author(s):  
Tuomo Kuusi ◽  
Mikko Parviainen
Keyword(s):  
Cauchy Problem ◽  
Degenerate Cauchy Problem

Generalized nonhomogeneous abstract degenerate Cauchy problem

2013 ◽  
Vol 7 ◽  
pp. 2441-2453
Author(s):  
Susilo Hariyanto ◽  
Lina Aryati ◽  
Widodo
Keyword(s):  
Cauchy Problem ◽  
Degenerate Cauchy Problem

On the Degenerate Cauchy Problem

1965 ◽  
Vol 17 ◽  
pp. 245-256 ◽  
Author(s):  
R. W. Carroll ◽  
C. L. Wang
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Mixed Type ◽  
Abstract Version ◽  
Hyperbolic Region ◽  
The Cauchy Problem ◽  
Equation Of Mixed Type ◽  
Image Position ◽  
Complete Bibliography ◽  
Degenerate Cauchy Problem

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)

A Uniqueness Theorem on the Degenerate Cauchy Problem(1)

1975 ◽  
Vol 18 (3) ◽  
pp. 417-421 ◽  
Author(s):  
Chung-Lie Wang
Keyword(s):  
Hilbert Space ◽  
Cauchy Problem ◽  
Uniqueness Theorem ◽  
Separable Hilbert Space ◽  
Adjoint Operator ◽  
Continuous Linear ◽  
Linear Maps ◽  
Image Position ◽  
Degenerate Cauchy Problem ◽  
Densely Defined

In [4] Carroll and the author have treated the following problem(1)where Λ is a closed densely defined self-adjoint operator in a separable Hilbert space H with (Λu, u) ≥ c ‖u‖2, c > 0, Λ-1 ∊ L(H) (L(E, F) is the space of continuous linear maps from E to F; in particular, L(H) = L(H, H)), a(t) > 0 for t > 0 a(0) = 0 and S(t), R(t), B(t) ∈ L(H).

scholarly journals The Solution Of Nonhomogen Abstract Cauchy Problem by Semigroup Theory of Linear Operator

2017 ◽  
Vol 2 (2) ◽  
pp. 143
Author(s):  
Susilo Hariyanto
Keyword(s):  
Hilbert Space ◽  
Cauchy Problem ◽  
Linear Operator ◽  
Infinitesimal Generator ◽  
Original Problem ◽  
Semigroup Theory ◽  
Abstract Cauchy Problem ◽  
Direct Sum ◽  
Special Operator ◽  
Degenerate Cauchy Problem

<div style="text-align: justify;">In this article we will investigate how to solve nonhomogen degenerate Cauchy problem via theory of semigroup of linear operator. The problem is formulated in Hilbert space which can be written as direct sum of subset Ker M and Ran M*. By certain assumptions the problem can be reduced to nondegenerate Cauchy problem. And then by composition between invers of operator M and the nondegenerate problem we can transform it to canonic problem, which is easier to solve than the original problem. By taking assumption that the operator A is infinitesimal generator of semigroup, the canonic problem has a unique solution. This allow to define special operator which map the solution of canonic problem to original problem. ©2016 JNSMR UIN Walisongo. All rights reserved.</div>

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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