Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1)

This abstract booklet includes the abstracts of the papers that have been presented at International Conference on Mathematics and its Applications in Science and Engineering (ICMASE 2020) which is held in Ankara Hacı Bayram Veli University, Ankara, Turkey between 9-10 July, 2020, via Online because of Covid 19 pandemia. The aim of this conference is to exchange ideas, discuss developments in mathematics, develop collaborations and interact with professionals and researchers from all over the world in with some of the following interesting topics: Functional Analysis, Approximation Theory, Real Analysis, Complex Analysis, Harmonic and non-Harmonic Analysis, Applied Analysis, Numerical Analysis, Geometry, Topology and Algebra, Modern Methods in Summability and Approximation, Operator Theory, Fixed Point Theory and Applications, Sequence Spaces and Matrix Transformation, Modern Methods in Summability and Approximation, Spectral Theory and Diferantial Operators, Boundary Value Problems, Ordinary and Partial Differential Equations, Discontinuous Differential Equations, Convex Analysis and its Applications, Optimization and its Application, Mathematics Education, Application on Variable Exponent Lebesgue Spaces, Applications on Differential Equations and Partial Differential Equations, Fourier Analysis, Wavelet and Harmonic Analysis Methods in Function Spaces, Applications on Computer Engineering, Flow Dynamics. However, the talks are not restricted to these subjects only. I am pleased to tell that this conference is also organized as a final multiplier event of the Rules_Math Project, supported by the EU.

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SOME PARTIAL DIFFERENTIAL EQUATIONS IN BANACH SPACES

Real Analysis Exchange ◽

10.2307/44151497 ◽

1979 ◽

Vol 5 (1) ◽

pp. 132

Author(s):

Welland

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Banach Spaces ◽

Partial Differential

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On the theory and practice of thin-walled structures

Georgian Mathematical Journal ◽

10.1515/gmj-2020-2089 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Tamaz Vashakmadze

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Boundary Conditions ◽

Complex Analysis ◽

Theory And Practice ◽

Linear Case ◽

Wide Sense ◽

Partial Differential ◽

Thin Walled Structures ◽

Thin Walled

Abstract The basic problem of satisfaction of boundary conditions is considered when the generalized stress vector is given on the surfaces of elastic plates and shells. This problem has so far remained open for both refined theories in a wide sense and hierarchic type models. In the linear case, it was formulated by I. N. Vekua for hierarchic models. In the nonlinear case, bending and compression-expansion processes do not split and in this context the exact structure is presented for the system of differential equations of von Kármán–Mindlin–Reisner (KMR) type, constructed without using a variety of ad hoc assumptions since one of the two relations of this system in the classical form is the compatibility condition, but not the equilibrium equation. In this paper, a unity mathematical theory is elaborated in both linear and nonlinear cases for anisotropic inhomogeneous elastic thin-walled structures. The theory approximately satisfies the corresponding system of partial differential equations and the boundary conditions on the surfaces of such structures. The problem is investigated and solved for hierarchic models too. The obtained results broaden the sphere of applications of complex analysis methods. The classical theory of finding a general solution of partial differential equations of complex analysis, which in the linear case was thoroughly developed in the works of Goursat, Weyl, Walsh, Bergman, Kolosov, Muskhelishvili, Bers, Vekua and others, is extended to the solution of basic nonlinear differential equations containing the nonlinear summand, which is a composition of Laplace and Monge–Ampére operators.

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