In this paper, we study the initial-boundary value problem of 3D incompressible Kelvin-Voigt-Cahn-Hilliard system for the case of initial density away from zero. We construct a new blow-up mechanism of strong solution.
We prove the short-time asymptotic formula for the interfaces and local solutions near the interfaces for the nonlinear double degenerate reaction–diffusion equation of turbulent filtration with strong absorption ut=(|(um)x|p−1(um)x)x−buβ,mp>1,β>0.Full classification is pursued in terms of the nonlinearity parameters m,p,β and asymptotics of the initial function near its support. Numerical analysis using a weighted essentially nonoscillatory (WENO) scheme with interface capturing is implemented, and comparison of numerical and analytical results is presented.
In this paper we prove the existence of finite traveling-wave type solutions to the nonlinear double degenerate parabolic equation of turbulent filtration with absorption.
The study is concerned with the application of a novel idea used to find analytical solutions of a nonlinear boundary value problem that arises in channel flow problems. The velocity profile of a viscoelastic fluid between two planes is obtained with both slip and no-slip boundary conditions. We present analytical solutions on classical problems – the Poiseuille flow, and the generalized Couette flow of a viscoelastic fluid between two parallel planes. The viscoelastic fluid is modeled by an Oldroyd 6-constant fluid, giving rise to a highly nonlinear ordinary differential equation. This equation has been solved via a novel approach by reducing the differential equation to a cubic algebraic equation, giving rise to a non-recursive series solution to the equation. Finally, after the solution of the general differential equation is given Newton’s Method is used for faster convergence to solve the equation in the case of three common boundary conditions.
In this paper, we study the Cauchy problem for a two-species chemotaxis model in R N for N ≥ 2. We prove the global well-posedness with small initial data in Besov-Morrey spaces.
In this paper, we study the Cauchy problem for a chemotaxis-fluid model with the logarithmic sensitivity function in spatial dimensions two. We establish a continuation criteria of the smooth solution.
This paper concentrates on the comparison theorems for generalized Caputo fractional differential equations of arbitrary order α (0 ≤ n − 1 < α ≤ n ) under strict and nonstrict inequalities primarily. Firstly, comparison theorems for the generalized Caputo fractional differential equations is proved when the functions in equations satisfy some strict inequalities. We also consider comparison results for the generalized Caputo fractional differential equations when the functions in equations satisfy some nonstrict inequalities.
The present study investigates certain singular Initial-Value Problems (IVPs) featuring the classical and generalized inhomogeneous Lane-Emden-type equations. These equations are very important models as they appear in many physical applications, including thermodynamics to mention a few. Further, the study proposes different forms of inverse integral operators that are based on the Adomian method to accelerate the convergence rate of the standard Adomian Decomposition Method (ADM). The method is then applied to various types of linear and nonlinear test problems and was found to be an effective modification by monitoring the rapidity of the convergence rate.
In this paper, the boundary value problem of a class of nonlinear singular impulsive differential equations in Banach space is studied. By constructing a special cone and defining a special operator, the impulsive problem is transformed into a continuous problem. By using the fixed point theorem of cone extension and cone compression, the existence of multiple positive solutions is obtained.
Many evolutionary positive control systems can be described by an abstract Cauchy problem governed at the boundary. Using the semigroup approach, we define and characterize the positive boundary robust stability. In order to illustrate the theoretical results, an applications to an age dependant population equation is considered. Mathematics Subject Classification: 93B05, 93B35, 93B52, 93D15, 46B42
In this paper, we use Mawhin’s continuous theorem to discuss the sufficient conditions for the existence and uniqueness of an w-periodic solution for a kind of third-order neutral functional differential equation of the form d3 dt3 (x(t)−d(t)x(t−δ))+a(t)h(t, x(t))+b(t)f(t, x(t))+c(t)g(t, x(t−r(t))) = p(t) Mathematics Subject Classification: 34C25
In this paper, we establish some new convergence theorems forMT functions. By applying our new convergence theorems, we obtain some new fixed point theorems. Mathematics Subject Classification: 41A52, 41A65, 47H10, 54H25
The main aim of this paper, is to discuss the stochastic asymptotic stability of the zero solution for certain third-order stochastic delay differential equations with Itô’s formula by constructing a Lyapunov functionals.
The class of nonlinear partial differential equations that can be decomposed into sums of terms that are products of not necessarily the same number of linear differential operators is considered. Necessary and sufficient conditions for an arbitrary linear combination of a finite and an infinite number of solutions to satisfy the equation are derived. Mathematics Subject Classification: 35G20, 35G31, 35G99
In this paper, we consider the Keller-Segel system coupled with the Navier-Stokes equations fluid in R2. A blow-up criterion of the smooth solution of the model is given.
This note complements a previous paper by the author in two ways. Firstly errors in this previous paper for the sufficient conditions for sums of two solutions of specific equations to satisfy the equation are underlined. Secondly, in this work, the class of nonlinear partial differential equations that can be decomposed into sums of terms that are products of not necessarily the same number of linear partial differential operators is considered and necessary and sufficient conditions on the operators and on the solutions are established for the linear combinations of two solutions to satisfy the equation. In the mentioned previous paper a necessary and sufficient condition was obtained for the same superposition property for equations that are composed of sums of products of the same number of linear partial differential operators. Also an example is included for the problem taken up.
