An inverse problem for a 2D parabolic equation with nonlocal overdetermination condition N. Ye. Kinash

Abstract

We consider an inverse problem of identifying the time-dependent coefficient $a(t)$ in a two-dimensional parabolic equation: $$u_t=a(t)\Delta u+b_1(x,y,t)u_x+b_2(x,y,t)u_y+c(x,y,t)u+f(x,y,t),\,(x,y,t)\in Q_T,$$ with the initial condition, Neumann boundary data and the nonlocal overdetermination condition $$\nu_1(t)u(0,y_0,t)+\nu_2(t)u(h,y_0,t)=\mu_3(t),\quad t\in[0,T],$$ where $y_0$ is a fixed number from $[0,l].$ The conditions of existence and uniqueness of the classical solution to this problem are established. For this purpose the Green function method, Schauder fixed point theorem and the theory of Volterra intergral equations are utilized.

Authors and Affiliations

N. Ye. Kinash

Keywords

Related Articles

On estimates for the Jacobi transform in the space Lp(R+,Jα,β(x)dx)

In this paper, we prove the estimates for the Jacobi transform in Lp(R+,Jα,β(x)dx) as applied to some classes of functions characterized by a generalized modulus of continuity.

ON A COMPLETE TOPOLOGICAL INVERSE POLYCYCLIC MONOID

We give sufficient conditions when a topological inverse l-polycyclic monoid Pl is absolutely Hclosed in the class of topological inverse semigroups. For every infinite cardinal l we construct the coarsest semigroup inve...

Green-Rvachev's quasi-function method for constructing two-sided approximations to positive solution of nonlinear boundary value problems

A homogeneous Dirichlet problem for a semilinear elliptic equations with the Laplace operator and Helmholtz operator is investigated. To construct the two-sided approximations to a positive solution of this boundary valu...

Permanence of a discrete predator-prey system with nonmonotonic functional responses and endless delay

A discrete-time analogue of predator-prey model with nonmonotonic functional responses and endless delay is considered in the paper. We investigate the question of obtaining conditions of permanent behavior of the dynami...

On Feller semigroup generated by solution of nonlocal parabolic conjugation problem

The paper deals with the problem of construction of Feller semigroup for one-dimensional inhomogeneous diffusion processes with membrane placed at a point whose position on the real line is determined by a given function...

Download PDF file
  • EP ID EP262976
  • DOI 10.15330/cmp.8.1.107-117
  • Views 81
  • Downloads 0

How To Cite

N. Ye. Kinash (2016). An inverse problem for a 2D parabolic equation with nonlocal overdetermination condition N. Ye. Kinash. Карпатські математичні публікації, 8(1), 107-117. https://europub.co.uk/articles/-A-262976