Stanisław Brzychczy
(1996)
We consider a nonlinear differential-functional parabolic boundary initial value problem
(1)
⎧A z + f(x,z(t,x),z(t,·)) - ∂z/∂t = 0 for t > 0, x ∈ G,
⎨z(t,x) = h(x) for t > 0, x ∈ ∂G,
⎩z(0,x) = φ₀(x) for x ∈ G,
and the associated elliptic boundary value problem with Dirichlet condition
(2)
⎧Az + f(x,z(x),z(·)) = 0 for x ∈ G,
⎨z(x) = h(x) for x ∈ ∂G
⎩
where , G is an open and bounded domain with (0 < α ≤ 1) boundary, the operator
Az := ∑j,k=1m ajk(x) (∂²z/(∂xj...