scholarly journals On mathematical modelling of temporal spatial spread of epidemics

2020 ◽  
Vol 15 ◽  
pp. 6
Author(s):  
Kh.A. Khachatryan ◽  
A.Zh. Narimanyan ◽  
A.Kh. Khachatryan
Keyword(s):  
Integral Equation ◽  
Mathematical Modelling ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Spatial Spread ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Convergence Results ◽  
Integral Differential Equations ◽  
Multidimensional Integral

In the present work a generalized epidemic model containing a system of integral-differential equations is described. Using different transformations the system is reduced to a single nonlinear multidimensional integral equation. For the obtained equation the existence and uniqueness results are proved. Based on theoretical convergence results several application examples are presented with corresponding numerical results.

scholarly journals Existence and Uniqueness of the Solution for an Integral Equation with Supremum, via w-Distances

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1554 ◽  
Author(s):  
Veronica Ilea ◽  
Diana Otrocol
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Stability Result ◽  
Fixed Point Problem ◽  
Comparison Theorems ◽  
Point Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Uniqueness Of The Solution

Following the idea of T. Wongyat and W. Sintunavarat, we obtain some existence and uniqueness results for the solution of an integral equation with supremum. The paper ends with the study of Gronwall-type theorems, comparison theorems and a result regarding a Ulam–Hyers stability result for the corresponding fixed point problem.

A 1D MODEL FOR A CLOSED RIGID FILAMENT IN STOKES FLOW

2009 ◽  
Vol 19 (06) ◽  
pp. 911-937
Author(s):  
PH. CAUSSIGNAC
Keyword(s):  
Integral Equation ◽  
Fluid Velocity ◽  
Single Layer ◽  
Numerical Convergence ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Convergence Results ◽  
1D Model ◽  
Resistance Matrix ◽  
Set Up

We adapt an existing asymptotic method to set up a one-dimensional model for the fall of a closed filament in an infinite fluid in the Stokes regime. Starting from the single-layer integral representation of the fluid velocity around the filament, we get, for a very slender filament, a Fredholm integral equation on the filament centerline. From this equation, we can compute the drag and force acting on the filament and consequently the resistance matrix. The integral equation is discretized with a collocation method. The study of a scalar model problem yields existence and uniqueness results together with an error estimate for the discretization scheme. Then, we compare the resistance matrix of thin ideal knots obtained from the discretization of the present model to a boundary element method; numerical convergence results and a good agreement of both methods validate our model.

scholarly journals ON A CLASS OF SADDLE POINT PROBLEMS AND CONVERGENCE RESULTS

2020 ◽  
Vol 25 (4) ◽  
pp. 608-621
Author(s):  
Mariana Chivu Cojocaru ◽  
Andaluzia Matei
Keyword(s):  
Saddle Point ◽  
Existence And Uniqueness ◽  
Nonlinear Term ◽  
Point Theory ◽  
Saddle Point Problems ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Convergence Results ◽  
Uniqueness Of The Solution ◽  
Mixed Variational Problem

We consider an abstract mixed variational problem consisting of two inequalities. The first one is governed by a functional φ, possibly non-differentiable. The second inequality is governed by a nonlinear term depending on a non negative parameter ǫ. We study the existence and the uniqueness of the solution by means of the saddle point theory. In addition to existence and uniqueness results, we deliver convergence results for ǫ → 0. Finally, we illustrate the abstract results by means of two examples arising from contact mechanics.

Birkhoff Interpolation at the nth Roots of Unity: Convergence

1981 ◽  
Vol 33 (2) ◽  
pp. 362-371 ◽  
Author(s):  
S. D. Riemenschneider ◽  
A. Sharma
Keyword(s):  
Convergence Theorem ◽  
Existence And Uniqueness ◽  
Roots Of Unity ◽  
Second Derivative ◽  
Existence And Uniqueness Theorem ◽  
Birkhoff Interpolation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Convergence Results ◽  
Special Cases

The first investigations on this type of problem were carried out by O. Kiš [2]. Kiš considered the problem of interpolating a function and its second derivative at the nth roots of unity (the (0, 2) problem) by 2n – 1 degree polynomials, and the convergence of such approximates. Later, Sharma [8], [9] extended the existence and uniqueness results to (0, m) interpolation, and essentially to (0, m1, m2) interpolation. In the latter case, Sharma established the convergence results for (0, 2, 3), (0, 1, 3) and (0, 1, 4) interpolation as well. Although some further special cases were considered [10] these were the essential results until very recently. Now Cavaretta, Sharma and Varga [1] have established the existence and uniqueness theorem for all possible interpolations of this type (see Theorem 2.1 below). Motivated by the work of Cavaretta, Sharma and Varga and the earlier work of Sharma [9], a different proof of this result is provided, and this proof is used to establish a convergence theorem in the general case.

scholarly journals Sensitivity analysis of solutions for a system of generalized parametric nonlinear quasivariational inequalities

2005 ◽  
Vol 2005 (11) ◽  
pp. 1795-1807
Author(s):  
Zeqing Liu ◽  
Beibei Zhu ◽  
Shin Min Kang ◽  
Gwang Il Kim
Keyword(s):  
Sensitivity Analysis ◽  
Existence And Uniqueness ◽  
Maximal Monotone ◽  
Iterative Sequence ◽  
Monotone Mappings ◽  
Quasivariational Inequalities ◽  
Existence And Uniqueness Results ◽  
New Class ◽  
Uniqueness Results ◽  
Convergence Results

A new class of system of generalized parametric nonlinear quasivariational inequalities involving various classes of mappings is introduced and studied. With the properties of maximal monotone mappings, the equivalence between the class of system of generalized parametric nonlinear quasivariational inequalities and a class of fixed point problems is proved and an iterative algorithm with errors is constructed. A few existence and uniqueness results and sensitivity analysis of solutions are also established for the system of generalized nonlinear parametric quasivariational inequalities and some convergence results of iterative sequence generated by the algorithm with errors are proved.

scholarly journals Existence and Uniqueness Results for a Smooth Model of Periodic Infectious Diseases

2016 ◽  
Vol 2016 ◽  
pp. 1-4
Author(s):  
Guy Degla
Keyword(s):  
Integral Equation ◽  
Asymptotic Stability ◽  
Existence And Uniqueness ◽  
Bounded Solution ◽  
Stability Result ◽  
Implicit Function ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Small Delay ◽  
Smooth Model

We prove the existence of a curve (with respect to the scalar delay) of periodic positive solutions for a smooth model of Cooke-Kaplan’s integral equation by using the implicit function theorem under suitable conditions. We also show a situation in which any bounded solution with a sufficiently small delay is isolated, clearing an asymptotic stability result of Cooke and Kaplan.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

scholarly journals BSDEs with polynomial growth generators

2000 ◽  
Vol 13 (3) ◽  
pp. 207-238 ◽  
Author(s):  
Philippe Briand ◽  
René Carmona
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Polynomial Growth ◽  
Probabilistic Representation ◽  
Existence And Uniqueness Results ◽  
State Variable ◽  
Cahn Equation ◽  
Uniqueness Results ◽  
Terminal Time

In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

Nontrivial solutions of non-autonomous dirichlet fractional discrete problems

2020 ◽  
Vol 23 (4) ◽  
pp. 980-995
Author(s):  
Alberto Cabada ◽  
Nikolay Dimitrov
Keyword(s):  
Existence And Uniqueness ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Fractional Difference ◽  
Nonlinear Part ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Difference Equation ◽  
Discrete Problems ◽  
Series Of Functions

AbstractIn this paper, we introduce a two-point boundary value problem for a finite fractional difference equation with a perturbation term. By applying spectral theory, an associated Green’s function is constructed as a series of functions and some of its properties are obtained. Under suitable conditions on the nonlinear part of the equation, some existence and uniqueness results are deduced.

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