Related papers: Nonlocal and multipoint boundary value problems fo…
In this work two-point boundary value problem for one class of second order ordinary differential equations with variable coefficients is solved.
The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the…
In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
We consider a wide class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the normed complex space $(C^{(n)})^m$ of $n\geq r$ times continuously differentiable…
We study a nonlocal balance equation that describes the evolution of a system consisting of infinitely many identical particles those move along a deterministic dynamics and can also either disappear or give a spring. In this case, the…
A general, uniform, rigorous and constructive thermodynamic approach to weakly nonlocal non-equilibrium thermodynamics is reviewed. A method is given to construct and restrict the evolution equations of physical theories according to the…
We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time. We prove the equivalence of this Stefan problem with a class of boundary value problems…
The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a…
Since the order of elliptic type model equation (Laplace equation) is two [1], [2], then it is natural the order of composite type model equation must be [3] [4] [5] three. At each point of the domain under consideration these equations…
We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms…
In the present work we investigate a boundary problem with non-local conditions, connecting values of seeking function on various characteristics for parabolic-hyperbolic equation with three lines of type changing. The considered problem is…
We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary…
In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…
In the paper, we investigate the nonlinear thermoelasticity model in two- and three-dimensional convex and bounded domains. We propose new boundary conditions for the displacement. These conditions are not usual in thermoelasticity.…
We give an explicit representation of the fundamental solution to the heat equation on a half-space of ${\mathbb R}^N$ with the homogeneous dynamical boundary condition, and obtain upper and lower estimates of the fundamental solution.…
The classical half line Robin problem for the heat equation may be solved via a spatial Fourier transform method. In this work, we study the problem in which the static Robin condition $bq(0,t)+q_x(0,t)=0$ is replaced with a dynamic Robin…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
In this paper we prove the existence and uniqueness of the solution of a non-stationary problem that modelizes the behaviour of the concentrations and the temperature of gases going through a cylindrical passage of an automotive catalytic…
The unified transform method introduced by Fokas can be used to analyze initial-boundary value problems for integrable evolution equations. The method involves several steps, including the definition of spectral functions via nonlinear…
Existence and uniqueness of solutions for $\alpha\in\left( 2,3\right] $ order fractional differential equations with three point fractional boundary and integral conditions is discussed. The results are obtained by using standard fixed…