5 research outputs found
Regularity properties of degenerate convolution-elliptic equations
Get PDFThe coercive properties of degenerate abstract convolution-elliptic equations are
investigated. Here we find sufficient conditions that guarantee the separability of
these problems in Lp spaces. It is established that the corresponding
convolution-elliptic operator is positive and is also a generator of an analytic
semigroup. Finally, these results are applied to obtain the maximal regularity
properties of the Cauchy problem for a degenerate abstract parabolic equation in
mixed Lp norms, boundary value problems for degenerate integro-differential
equations, and infinite systems of degenerate elliptic integro-differential equations
Nonlocal separable elliptic equations and applications
No full textThe regularity properties of nonlo cal elliptic equations are investigated in abstract weighted Lp spaces. Here, we find sufficient conditions that guarantee the separability of the linear problems. We prove that the corresponding nonlo cal elliptic operator is sectorial and is also a negative generator of an analytic semigroup. In application, the maximal regularity properties of the for degenerate abstract equation in LP norms, and infinite systems of degenerate elliptic integro-differential equations with parameters are obtained.No sponso
Estimates for the abstract Boussinesq equations
Get PDFIn this paper, the existence and uniqueness of the solution of the integral
boundary value problem for abstract Boussinesq equations are obtained. The
equations include a linear operator A defined in a Banach space E, in which
by choosing E and A we can obtain numerous classes of nonlocal initial value
problems for Boussinesq equations which occur in a wide variety of physical
systems
Maximal Regular Convolution-Differential Equations in Weighted Besov Spaces
No full textBy using Fourier multiplier theorems, the maximal regularity properties of abstract convolution differential equations in weighted Besov spaces are investigated. It is shown that the corresponding convolution differential operators are positive and generate analytic semi groups in abstract Besov spaces. Then, the well-posedness of the Cauchy problem for parabolic convolution operator equation is established. Moreover, these results are used to establish maximal regularity properties for system of integro-differential equations of finite and infinite orders.Science Citation Index Expande
NONLOCAL PROBLEMS FOR BOUSSINESQ EQUATIONS
No full textIn this paper, the existence and uniqueness of solution of the integral boundary value problem for abstract Boussinesq equations are obtained. The equation includes a linear operator A defined in a Banach space E, in which by choosing E and A we can obtain numerous classes of nonlocal initial value problems for Boussinesq equations which occur in a wide variety of physical systems.Conference Proceedings Citation Index - Scienc
