SINGULAR INTEGRO-DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE AND INVERSE PROBLEMS

2003 ◽  
Vol 13 (12) ◽  
pp. 1745-1766 ◽  
Author(s):  
A. FAVINI ◽  
A. LORENZI
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Parabolic Type ◽  
Initial Boundary ◽  
Uniqueness Result ◽  
Initial Boundary Value Problems ◽  
First Order ◽  
Global Existence And Uniqueness ◽  
End Use ◽  
Initial Boundary Value

We prove a global existence and uniqueness result for the recovery of unknown scalar kernels in linear singular first-order integro-differential initial-boundary value problems in Banach spaces. To this end use is made of suitable weighted Lp-spaces. Finally, we give a few applications to explicit singular partial integro-differential equations of parabolic type.

scholarly journals On the Evolutionary Form of the Constraints in Electrodynamics

2018 ◽  
Author(s):  
István Rácz
Keyword(s):  
Existence And Uniqueness ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Uniqueness Of Solutions ◽  
Maxwell Theory ◽  
Constraint Equations ◽  
First Order ◽  
Global Existence And Uniqueness ◽  
Hyperbolic Form ◽  
Initial Boundary Value

The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a vector field" type constraints can always be put into linear first order hyperbolic form for which global existence and uniqueness of solutions to an initial-boundary value problem is guaranteed.

On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions

2022 ◽  
pp. 108128652110731
Author(s):  
Victor A Eremeyev ◽  
Leonid P Lebedev ◽  
Violetta Konopińska-Zmysłowska
Keyword(s):  
Weak Solution ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Equations Of Motion ◽  
Elastic Shell ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Finite Set ◽  
Initial Boundary Value ◽  
Small Deformations

The problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated and studied. It is proved a theorem of existence and uniqueness of a weak solution for the problem under consideration.

DYNAMICS OF MULTISECTION SEMICONDUCTOR LASERS

2005 ◽  
Vol 9 (1) ◽  
pp. 51-66 ◽  
Author(s):  
J. Sieber ◽  
M. Radžiūnas ◽  
K. R. Schneider
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Semiconductor Lasers ◽  
Invariant Manifolds ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Low Dimension ◽  
Global Existence And Uniqueness ◽  
Numerical Bifurcation ◽  
Initial Boundary Value

We investigate the longitudinal dynamics of multisection semiconductor lasers based on a model, where a hyperbolic system of partial differential equations is nonlinearly coupled with a system of ordinary differential equations. We present analytic results for that system: global existence and uniqueness of the initial‐boundary value problem, and existence of attracting invariant manifolds of low dimension. The flow on these manifolds is approximately described by the so‐called mode approximations which are systems of ordinary differential equations. Finally, we present a detailed numerical bifurcation analysis of the two-mode approximation system and compare it with the simulated dynamics of the full PDE model.

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