Browsing by Subject "uniqueness"

Now showing 1 - 14 of 14

Access status: Open Access ,
A finite difference method for nonlinear parabolic-elliptic systems of second-order partial differential equations
(2007) Malec, Marian; Sapa, Lucjan
This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations) and the other of the elliptic type (equations with a parameter) in a cube in $\mathbf{R}^{1+n}$. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.
Access status: Open Access ,
A unique weak solution for a kind of coupled system of fractional Schrödinger equations
(Wydawnictwa AGH, 2020) Abdolrazaghi, Fatemeh; Razani, Abdolrahman
In this paper, we prove the existence of a unique weak solution for a class of fractional systems of Schrödinger equations by using the Minty-Browder theorem in the Cartesian space. To this aim, we need to impose some growth conditions to control the source functions with respect to dependent variables.
Access status: Open Access ,
Boundary value problems for second order delay differential equations
(2012) Skóra, Lidia
We present some existence and uniqueness result for a boundary value problem for functional differential equations of second order.
Access status: Open Access ,
Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis
(2008) Jais, Mathias
We consider the solvability of the semilinear parabolic differential equation $\frac{\partial u}{\partial t}(x,t)- \Delta u(x,t) + c(x,t)u(x,t) = \mathcal{P}(u) + \gamma (x,t)$ in a cylinder $D=\Omega \times (0,T)$, where $\mathcal{P}$ is a hysteresis operator of Preisach type. We show that the corresponding initial boundary value problems have unique classical solutions. We further show that using this existence and uniqueness result, one can determine the properties of the Preisach operator $\mathcal{P}$ from overdetermined boundary data.
Access status: Open Access ,
Existence and uniqueness results for fractional differential equations with boundary value condition
(2011) Lv, LinLi; Wang, JinRong; Wei, Wei
In this paper, we study the existence and uniqueness of fractional differential equations with boundary value conditions. A new generalized singular type Gronwall inequality is given to obtain important a priori bounds. Existence and uniqueness results of solutions are established by virtue of fractional calculus and fixed point method under some weak conditions. An example is given to illustrate the results.
Access status: Restricted ,
Istnienie i jednoznaczność rozwiązania klasycznego układu ewolucyjnych równań różniczkowych
(Data obrony: 2017-07-10) Światłowska, Julita
Wydział Matematyki Stosowanej
Access status: Restricted ,
Metoda prostych dla różniczkowo-funkcyjnych równań parabolicznych
(Data obrony: 2017-07-18) Kądziela, Agnieszka
Wydział Matematyki Stosowanej
Access status: Open Access ,
On solvability of elliptic boundary value problems via global invertibility
(Wydawnictwa AGH, 2020) Bełdziński, Michał; Galewski, Marek
In this work we apply global invertibility result in order to examine the solvability of elliptic equations with both Neumann and Dirichlet boundary conditions.
Access status: Open Access ,
On unique solvability of a Dirichlet problem with nonlinearity depending on the derivative
(Wydawnictwa AGH, 2019) Bełdziński, Michał; Galewski, Marek
In this work we consider second order Dirichelet boundary value problem with nonlinearity depending on the derivative. Using a global diffeomorphism theorem we propose a new variational approach leading to the existence and uniqueness result for such problems.
Access status: Open Access ,
Positive solutions of arbitrary order nonlinear fractional differential equations with advanced arguments
(2011) Ntouyas, Sotiris K.; Wang, Guotao; Zhang, Lihong
In this paper, we investigate the existence and uniqueness of positive solutions to arbitrary order nonlinear fractional differential equations with advanced arguments. By applying some known fixed point theorems, sufficient conditions for the existence and uniqueness of positive solutions are established.
Access status: Open Access ,
Random integral equations on time scales
(2013) Lupulescu, Vasile; Lungan, Cristina
In this paper, we present the existence and uniqueness of random solution of a random integral equation of Volterra type on time scales. We also study the asymptotic properties of the unique random solution.
Access status: Open Access ,
Solutions of fractional nabla difference equations - existence and uniqueness
(2016) Jonnalagadda, Jagan Mohan
In this article, we discuss existence, uniqueness and dependency of solutions of nonlinear fractional nabla difference equations in a Banach space equipped with a suitable norm, using the contractive mapping approach. As an application of the established results we present and analyse a few examples.
Access status: Open Access ,
Uniqueness for a class p-Laplacian problems when a parameter is large
(Wydawnictwa AGH, 2024) Alreshidi, Bandar; Hai, D. D.
We prove uniqueness of positive solutions for the problem $-\Delta_{p}u=\lambda f(u)\text{ in }\Omega,\ u=0\text{ on }\partial \Omega,$ where $1\lt p\lt 2$ and $p$ is close to 2, $\Omega$ is bounded domain in $\mathbb{R}^{n}$ with smooth boundary $\partial \Omega$, $f:[0,\infty)\rightarrow [0,\infty )$ with $f(z)\sim z^{\beta }$ at $\infty$ for some $\beta \in (0,1)$, and $\lambda$ is a large parameter. The monotonicity assumption on $f$ is not required even for u large.
Access status: Open Access ,
Uniqueness of solution of a nonlinear evolution dam problem in a heterogeneous porous medium
(Wydawnictwa AGH, 2022) Attia, Messaouda Ben; Zaouche, Elmehdi; Bousselsal, Mahmoud
By choosing convenient test functions and using the method of doubling variables, we prove the uniqueness of the solution to a nonlinear evolution dam problem in an arbitrary heterogeneous porous medium of $\mathbb{R}^{n}$ ($n \in \{2,3\}$) with an impermeable horizontal bottom.