Non-simultaneous quenching in a system of heat equations coupled at the boundary

Non-simultaneous quenching in a system of heat equations coupled at the boundary

We study the solutions of a parabolic system of heat equations coupled at the boundary through a nonlinear flux. We characterize in terms of the parameters involved when nonsimultaneous quenching may appear. Moreover, if quenching is non-simultaneous we find the quenching rate, which surprisingly depends on the flux associated to the other component.

Incomplete quenching in a system of heat equations coupled at the boundary

In this paper we find a possible continuation for quenching solutions to a system of heat equations coupled at the boundary condition. This system exhibits simultaneous and non-simultaneous quenching. For non-simultaneous quenching our continuation is a solution of a parabolic problem with Neumann boundary conditions. We also give some results for simultaneous quenching and present some numeric...

Simultaneous versus Nonsimultaneous Blowup for a System of Heat Equations Coupled Boundary Flux

On Critical Exponents for a System of Heat Equations Coupled in the Boundary Conditions

In this paper, we consider the system ut = ∆u, vt = ∆v x ∈ R+ , t > 0, − ∂u ∂x1 = v, − ∂v ∂x1 = u x1 = 0, t > 0, u(x, 0) = u0(x), v(x, 0) = v0(x) x ∈ R+ , where R+ = {(x1, x′) | x′ ∈ RN−1, x1 > 0}, p, q > 0, and u0, v0 nonnegative. We prove that if pq ≤ 1 every nonnegative solution is global. When pq > 1 we let α = 1 2 p+1 pq−1 , β = 1 2 q+1 pq−1 . We show that if max(α, β) ≥ N 2 , all nontrivi...

The existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions

In this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. The differential operator is taken in the Riemann-Liouville sense. Applying the Schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system D^{alpha}_{0+}x(t)=fleft(t,y(t),D^{p}_{0+}y(t)right), t in (0,...