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On a Class of Parabolic Equations with Nonlocal Boundary Conditions by Hong-Ming Yin is a Mathematics article available to read on EtoBox.

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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.

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Author

Hong-Ming Yin

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-247X)

Published

2004

Language

EN

Field

Mathematics (Physical Sciences)