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

@inproceedings{Kordos2004OnUF,
  title={On Uniqueness for a System of Heat Equations Coupled in the Boundary Conditions},
  author={Mirosław Kordos},
  year={2004}
}
We consider the system ut =4u, vt =4v, 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 are positive numbers, and functions u0, v0 in the initial conditions are nonnegative and bounded. We show that nonnegative solutions are unique if pq > 1 or if (u0… CONTINUE READING