On a class of parabolic equations with nonlocal boundary conditions
Copyright policy )On a class of parabolic equations with nonlocal boundary conditions
The author considers the problem \[ \begin{aligned} &u_t = \nabla\cdot(d(x,t)\nabla u + \mathbf{W}(x,t)u), \quad (x,t)\in Q_T = \Omega\times(0,T],\\ &du_\nu + (\mathbf{W}\cdot\nu)u = \int_\Omega g(x,t,u)\,dx, \quad (x,t)\in S_T,\qquad u(x,0) = u_0(x), \quad x\in\Omega, \end{aligned} \] which is a generalized model for a theory of ion-diffusion in channels. Some conditions for the existence of a unique classical solution (local or global) are given. Also, the author considers the blow up conditions and the long-time behaviour to a corresponding linear problem.
- Washington State University United States
- Washington State University United States
- Washington University of St.Louis United States
Ion-transport model, blow up conditions, long-time behaviour, Nonlocal boundary conditions, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Reaction–diffusion equations, Applied Mathematics, Motion of charged particles, ion-diffusion in channels, Analysis
Ion-transport model, blow up conditions, long-time behaviour, Nonlocal boundary conditions, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Reaction–diffusion equations, Applied Mathematics, Motion of charged particles, ion-diffusion in channels, Analysis
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