On parabolic final value problems and well-posedness

Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators

The nonlocal boundary value problem for the parabolic differential equation v'(t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 < λ ≤ T in an arbitrary Banach space E with the dependent linear positive operator A(t) is investigated. The well-posedness of this problem is established in Banach spaces C 0 (β,γ) (E α-β ) of all E α-β -valued continuous functions φ(t) on [0, T] satisfying a Höld...

L-WELL-POSEDNESS OF 3D div-curl BOUNDARY VALUE PROBLEMS

Criteria for the existence and uniqueness of weak solutions of div-curl boundary-value problems on bounded regions in space with C-boundaries are developed. The boundary conditions are either given normal component of the field or else given tangential components of the field. Under natural integrability assumptions on the data, finite-energy (L) solutions exist if and only if certain compatibi...

Well-posedness of hyperbolic Initial Boundary Value Problems

Assuming that a hyperbolic initial boundary value problem satsifies an a priori energy estimate with a loss of one tangential derivative, we show a well-posedness result in the sense of Hadamard. The coefficients are assumed to have only finite smoothness in view of applications to nonlinear problems. This shows that the weak Lopatinskii condition is roughly sufficient to ensure well-posedness ...

The well-posedness of an anisotropic parabolic equation based on the partial boundary value condition

On the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equations

for the differential equation in a Hilbert space H with the self-adjoint positive definite operator A is considered. The well-posedness of this problem in Hölder spaces without a weight is established. The coercivity inequalities for solutions of the boundary value problem for elliptic-parabolic equations are obtained.