Related papers: Initial-boundary value problems for second order s…
This paper deals with numerical solutions to a partial differential equation of fractional order. Generally this type of equation describes a transition from anomalous diffusion to transport processes. From a phenomenological point of view,…
Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…
This paper develops a characterisation of when solutions of forced second order linear differential equations converge to the zero solution of the asymptotically stable and unforced second order equation, or when the solution is bounded,…
While it is known that one can consider the Cauchy problem for evolution equations with Caputo derivatives, the situation for the initial value problems for the Riemann-Liouville derivatives is less understood. In this paper we propose new…
In this article, we prove an existence of solutions for a non-local boundary value problem with nonlinearity in a nonlocal condition. Our method is based upon the Mawhin's coincidence theory.
A first-order ordinary differential equation, solved with respect to derivative, is considered. It's right-hand side is defined and continuous on the set, consisting of a connected open subset of a two-dimensional Euclidean space and a part…
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of…
This note is a description of some of the results obtained by the authors in connection with the problem in the title. These, discussed following a summary of background material concerning wedge differential operators, consist of the…
The aim of this work is to point out that the class of free boundary problems governed by second order autonomous ordinary differential equations can be transformed to initial value problems. Interest in the numerical solution of free…
Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…
This is a continuation of the first author's development of the theory of elliptic differential operators with edge degeneracies. That first paper treated basic mapping theory, focusing on semi-Fredholm properties on weighted Sobolev and…
This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of…
In this paper diffusion processes with changing modes are studied involving the variable order partial differential equations. We prove the existence and uniqueness theorem of a solution of the Cauchy problem for fractional variable order…
In this paper, we consider a class of initial-boundary value problems governed by pseudo-parabolic total variation flows. The principal characteristic of our problem lies in the velocity term of the diffusion flux, a feature that can bring…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the…
We study an initial-boundary value problem of variable-order time-fractional diffusion equations in one space dimension. Based on the wellposedness of the proposed model and the smoothing properties of its solutions, which are shown to be…
Second-order formulations of the 3+1 Einstein equations obtained by eliminating the extrinsic curvature in terms of the time derivative of the metric are examined with the aim of establishing whether they are well posed, in cases of…
We prove the existence of unique solutions to the Dirichlet boundary value problems for linear second-order uniformly parabolic operators in either divergence or non-divergence form with boundary blowup low-order coefficients. The domain is…
When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…