We derive the existence, uniqueness, and uniform Lp estimates for the abstract Navier– Stokes problem with small parameters in half-space. The equation involves small parameters and an abstract operator in a Banach space ...

In this paper, the Cauchy problem for linear and nonlinear wave equations is studied.The equation involves an abstract operator A in a Hilbert space H and a convolution term. Here, assuming sufficient smoothness on the ...

The maximal Bs p,q -regularity properties of a fractional convolution elliptic equation is studied. Particularly, it is proven that the operator generated by this nonlocal elliptic equation is sectorial in Bs p,q and ...

Here, we investigate Michaelis-Menten type dynamics of phase-space analysis to a mathematical model of tumor growth with an immune responses. We then explore the effects of adaptive cellular immunotherapy on the model ...

We study a nonlocal abstract Ginzburg-Landau type equation. The equation includes variable coefficients with convolution terms and an abstract linear operator function A in a Fourier-type Banach space E. For sufficiently ...

The Cauchy problem for linear and nonlinear Ginzburg-Landau type equations is studied. The equation includes variable coefficients with convolution terms. Assuming enough smoothness of the initial data and certain growth ...

In this paper, the integral problem for linear and nonlinear wave equations is studied. The equation involves abstract operator A in Hilbert space H. Here, assuming enough smoothness on the initial data and the operators, ...

In this paper, the spectral properties of linear operators in Banach spaces are studied. We find sufficient conditions on the structure of Banach spaces and resolvent properties that guarantee the completeness of the root ...

The abstract elliptic and parabolic equations on exterior regions are considered. The equations have top-order variable coefficients. The separability properties of boundary value problems for elliptic equation and ...

In this paper, we will show the properties of composition operators u → f (u) in framework of E-valued Sobolev and Lizorkin–Triebel spaces. Here E is a Banach space. Boundedness and continuity properties will be discussed ...