Finite Rank Solution for Conformable Degenerate First-Order Abstract Cauchy Problem in Hilbert Spaces

Singularly Perturbed Cauchy Problem for Abstract Linear Differential Equations of Second Order in Hilbert Spaces∗

We study the behavior of solutions to the problem { ε (u′′ ε (t) +A1uε(t)) + u ′ ε(t) +A0uε(t) = fε(t), t ∈ (0, T ), uε(0) = u0ε, uε(0) = u1ε, as ε → 0, where A1 and A0 are two linear self-adjoint operators in a Hilbert space H. MSC: 35B25, 35K15, 35L15, 34G10 keywords: singular perturbations; Cauchy problem; boundary layer function.

$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework

In the present work the space  $L_{p;r} $ which is continuously embedded into $L_{p} $  is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...

Inhomogeneous Two-Parameter Abstract Cauchy Problem

Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces

Existence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.