On a class of parabolic equations with nonlocal boundary conditions

By Hong-Ming Yin. 2004

95 citations recorded by the source corpus.

In this paper we study a class of parabolic equations subject to a nonlocal boundary condition. The problem is a generalized model for a theory of ion-diffusion in channels. By using energy method, we first derive some a priori estimates for solutions and then prove that the problem has a unique global solution. Moreover, under some assumptions on the nonlinear boundary condition, it is shown that the solution blows up in finite time. Finally, the long-time behavior of solution to a linear problem is also studied in the paper.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/92301879c88f17a58ea58145288a3d31d7f2a336

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Mehdi Dehghan
2. Ali Shokri
3. M. Tatari
4. Arezou Ghesmati
5. Abbas Saadatmandi
6. Mohsen Razzaghi
7. Mehdi Ramezani
8. Arturas Stikonas

In Computational Theory and Mathematics

1. Mehdi Dehghan
2. Feng Ding
3. Masoud Hajarian
4. Ali Shokri

In Numerical Analysis

1. Mehdi Dehghan
2. Ali Shokri
3. Mehrdad Lakestani
4. Abbas Saadatmandi
5. Arezou Ghesmati
6. Ali Lotfi
7. S. Yousefi
8. M. Tatari

Citations in the corpus

• A computational study of the one‐dimensional parabolic equation subject to nonclassical boundary specifications (2006, background): “The author of [49] has proved the existence, uniqueness, and continuous dependence of a strong solution upon the data for the following problem:”
• On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation (2005, background): “Bouziani also devoted a few papers to nonlocal problems for hyperbolic equations.”