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.

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 Initial boundary value problems for a fractional differential equation with hyper-Bessel operator

2018 ◽  
Vol 21 (1) ◽  
pp. 200-219 ◽  
Author(s):  
Fatma Al-Musalhi ◽  
Nasser Al-Salti ◽  
Erkinjon Karimov
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Initial Boundary ◽  
Fractional Diffusion ◽  
Initial Boundary Value Problems ◽  
Bessel Differential Operator ◽  
Fractional Differential ◽  
Inverse Source Problems ◽  
Initial Boundary Value

AbstractDirect and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart of a hyper-Bessel differential operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansions and results on existence and uniqueness are established. To solve the resultant equations, a solution to such kind of non-homogeneous fractional differential equation is also presented.

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