On boundary value problem for parabolic equations

On boundary value problem for fractional differential equations

In this paper‎, ‎we study the existence of solutions for a‎ ‎ fractional boundary value problem‎. ‎By using critical point theory‎ ‎ and variational methods‎, ‎we give some new criteria to guarantee‎ ‎ that‎ ‎ the problems have at least one solution and infinitely many solutions.

Initial - Boundary Value Problems for Parabolic Equations

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.

A Note on the Nonlocal Boundary Value Problem for Hyperbolic-parabolic Differential Equations

The nonlocal boundary value problem        d 2 u(t) dt 2 + Au(t) = f (t)(0 ≤ t ≤ 1), du(t) dt + Au(t) = g(t)(−1 ≤ t ≤ 0), u(−1) = αu (µ) + βu (λ) + ϕ, |α|, |β| ≤ 1, 0 < µ, λ ≤ 1 for differential equation in a Hilbert space H with the self-adjoint positive definite operator A is considered. The stability estimates for the solution of this problem are established. In applications, the stab...

Inverse boundary value problem for Maxwell equations

We prove a uniqueness theorem for an inverse boundary value problem for the Maxwell system with boundary data assumed known only in part of the boundary. We assume that the inaccessible part of the boundary is either part of a plane, or part of a sphere. This work generalizes the results obtained by Isakov [I] for the Schrödinger equation to Maxwell equations. Introduction. Let Ω ⊂ R be a bound...