Critical Exponents for a System of Heat Equations Coupled in a Non-linear Boundary Condition

Remarks on the blowup estimate for solution of the heat equation with a nonlinear boundary condition

“…where the constant c > 0 depends only on ⌦. A short proof of this fact can be found in [16]. It is also well known that for any > 0, 0  G N (x, y, t, ⌧ )  C N for |x y| , x, y 2 ⌦, 0 < ⌧ < t < T. (4.3)…”

Blow-up for a parabolic system coupled in an equation and a boundary condition

“…On the one hand, for problem (1.5) on B R = fjxj < Rg in the radially symmetric case, Deng [2] showed that if pq 6 1, all non-negative solutions are global, while if pq > 1, there are no non-trivial non-negative global solutions. Later, among other things, Deng [3] and Hu and Yin [11] independently extended this result to an arbitrary bounded domain « . On the other hand, arguing analogously as in [3], one can easily see that the result for (1.5) holds for problem (1.4).…”

Influence of variable coefficients on global existence of solutions of semilinear heat equations with nonlinear boundary conditions

“…with homogeneous Neumann boundary condition. We note that the Green's function has the following properties (see, for example, [24], [25]):…”