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Rishad Shahmurov

Publications and source records attributed to Rishad Shahmurov.

26 records · Page 2Linked to original sources
arXiv2019

The integral Cauchy problem for generalized Boussinesq equations with general leading parts

In this paper, the integral initial value problems for Boussinesq type equations are studied. The equation include the general differential operators. The existence, uniqueness and regularity properties of solution of these problems are obtained. By choosing differential operators including in the equation, the regularity properties of the Cauchy problem for different type of Boussinesg equations are studied.

math.AP↗
arXiv2017

Operator-valued multipliers in vector-valued weighted Besov spaces and applications

The operator-valued multiplier theorems in weighted abstract Besov spaces are studied. These results permit us to show embedding theorems in weighted Besov-Lions type spaces. The most regular class of interpolation space is found such that the mixed differential operator is bounded from Besov-Lions space to this and Ehrling-Nirenberg-Gagliardo type sharp estimates are established. By using these results the separability properties of degenerate differential operators are studied. Especially, we prove that the associated differential operators are positive and also are generators of analytic semigroups. Moreover, regularity properties for abstract elliptic equation, Cauchy problem for degenerate abstract parabolic equation and the infinite systems of degenerate parabolic equations are studied.

math.AP↗
arXiv2009

On Integral Operators with Operator Valued Kernels

Here Lq-Lp boundedness of integral operator with operator-valued kernels is studied and the main result is applied to convolution operators. Using these results Besov space regularity for Fourier multiplier operator is established.

math.FA↗
arXiv2009

Lp regularity for convolution operator equations in Banach spaces

Here we utilize operator--valued Lq-Lp Fourier multiplier theorems to establish lower bound estimates for large class of elliptic integro-differential equations in Rd. Moreover, we investigate separability properties of parabolic convolution operator equations that arise in heat conduction problems in materials with fading memory. Finally, we give some remarks on optimal regularity of elliptic differential equations and Cauchy problem for parabolic equations.

math.AP↗
arXiv2009

Linear and nonlinear convolution operator equations on the infinite strip

In the present paper we characterize the existence and uniqueness of maximal Lp-regular solutions of high order convolution operator equations. Particularly, we get coercive uniform estimates with respect to spectral parameter and we show that corresponding realization operator is R-positive and generates analytic semigroup in Lp. Then we apply these results to various problems of nonlinear integro-differential equations.

math.AP↗
arXiv2008

General Hormander and Mikhlin conditions for multipliers of Besov spaces

Here a new condition for the geometry of Banach spaces is introduced and the operator--valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hormander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equations are investigated.

math.FA↗
arXiv2008

Operator-valued Fourier multipliers in Besov spaces and its applications

The present paper, is devoted to investigation of operator--valued Fourier multiplier theorems from $B_{q_{1},r}^{s}$ to $B_{q_{2},r}^{s}$, optimal embedding of Besov spaces, the separability and positivity of differential operators. Here, we show that these differential operators generate analytic semigroup.

math.FA↗