Abstract
In present paper, we consider a problem with nonlocal conditions for parabolic equation and show that there exists a unique weak solution in Sobolev space. The main tool to prove the existence of a unique weak solution to the problem is a priori estimates derived by authors. We also note a connection between Steklov nonlocal conditions and first kind integral conditions. This connection enables interpret the problem under consideration as a problem with perturbed Steklov nonlocal conditions. Obtained results may be useful for certain class of problems including inverse problems.
Publisher
Samara State Technical University
Subject
Applied Mathematics,Mechanics of Materials,Condensed Matter Physics,Mathematical Physics,Modeling and Simulation,Software,Analysis
Reference22 articles.
1. The solution of the heat equation subject to the specification of energy
2. A boundary value problem in the theory of heat conduction with a nonclassical boundary condition
3. Ionkin N. I. The solution of a certain boundary value problem of the theory of heat conduction with a nonclassical boundary condition, Differ. Uravn., 1977, vol. 13, no. 2, pp. 294–304 (In Russian).
4. Kartynnik A. V. A three-point mixed problem with an integral condition with respect to the space variable for second-order parabolic equations, Differ. Equ., 1990, vol. 26, no. 9, pp. 1160–1166.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献