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

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

Blowup for a Non-Newtonian Polytropic Filtration System Coupled via Nonlinear Boundary Flux

We study the global existence and the global nonexistence of a non-Newtonian polytropic filtration system coupled via nonlinear boundary flux. We first establish a weak comparison principle, then discuss the large time behavior of solutions by using modified upper and lower solution methods and constructing various upper and lower solutions. Necessary and sufficient conditions on the global exi...

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.

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,...

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...