This work is devoted to the investigation of direct and inverse problems with nonlinear gluing condition for a mixed parabolic-hyperbolic equation involves Riemann-Liouville time fractional derivatives.The problem is reduced to study nonlinear Volterra integral equations.The methods of integral equations and successive approximations are used in proving theorems on existence and uniqueness.
In this work, we consider a transmission problem for an elastic-thermoelastic bar with the elastic part being surrounded by two thermoelastic parts in the presence of an infinite distributed delay term.The heat flux of the system is governed by Cattaneo's law.Under suitable assumption on the weight of the delay, we establish the polynomial stability of the solution by introducing a suitable Lyapunov functional.
A complete asymptotic solution of the boundary value problem in an infinite strip is constructed for a one-characteristic third-order equation degenerating into an elliptic equation, and the remainder is estimated.
In this paper, we consider a nonlocal boundary value problem for a multidimensional linear parabolic equation containing the integral of the desired solution.The coefficients of the considered parabolic equation are discontinious functions.The integral boundary condition represents the relationship that binds the value of the derivative of the desired solution with respect to the spatial variables at the boundary points and the value of the solution in the internal area.By using Galerkin method the existence of the generalized solution from V 1,0 2 (Q T ) is proved.The energy inequality is obtained and the uniqueness of the generalized solution is proved.It is proved that for many strong assumptions about the data of the problem, the generalized solution from V 1,0 2 (Q T ) belongs to space W 1,1 2 (Q T ).
On the R d the Dunkl operators D k,j d j=1 are the differential-difference operators associated with the reflection group Z d 2 on R d .We study some embeddings into the total Morrey space (D ktotal Morrey space) L p,λ,µ (µ k ), 0 ≤ λ, µ < d + 2γ k associated with the Dunkl operator on R d .These spaces generalize the Morrey spaces associated with the Dunkl operator on R d (D k -Morrey space) so that L p,λ (µ k ) ≡ L p,λ,λ (µ k ) and the modified Morrey spaces associated with the Dunkl operator on R d (modified D k -Morrey space) so that L p,λ (µ k ) ≡ L p,λ,0 (µ k ).
In this paper we consider the anisotropic maximal commutator Mbd and the commutator of the anisotropic maximal operator [b, Md] on the anisotropic total Morrey spaces Ldp,lambda,mu (IIBn). We obtain necessary and sufficient conditions for the boundedness of the operators Mbd and [b, Md] on Ldp,lambda,mu (IIBn) when b belongs to the bounded mean oscillation space BMO(IIBn). We also obtain new characterizations for some subclasses of BMO(IIBn).
In the present work we consider a new type of homogenous Fredholm integral equations (or limit integral equations).We study the question on transference of homogenous case of Fredholm theory to the Bohr spaces.As in the ordinary case, we establish that for every characteristic number corresponding subspace of solutions has finite dimension.For symmetric kernel we establish expansion of the kernel.
In this work, the existence of the fixed points of the mappings does independent of their smoothness, of the single-value or multi-value using a new geometrical approach is studied.Here, the fixed-point theorems are proved, which generalize the fixed-point theorems of Brouwer and Schauder, and also Kakutani, in some sense.This approach is based on the idea of the Poincare article [1] and the geometry of the image of mappings and is independent of the topological properties of spaces, which allows studying mappings acting in vector spaces.We studied the solvability of the nonlinear equations and inclusions by applying the obtained general results.Here some auxiliary results are obtained, also.
In this paper are proved the strong law of large numbers and the central limit theorem for the Markov random walks describes by the generalization autoregressive process of order one.
The paper investigates the properties of the Riemann function of the Cauchy problem for a second-order hyperbolic equation with a growing coefficient.The existence and uniqueness of the Riemann function are proved.Estimates are found for the Riemann function and its derivatives.
This work is dedicated to uncountable frames in non-separable Hilbert spaces associated with bilinear mappings.Bounded bilinear mapping is considered, and using this mapping, the concepts of uncountable b-Besselian system, b-frame and b-frame operator are introduced.Criteria for uncountable b-Besselness and b-frameness of system are proved, and some properties of uncountable b-frame operator are established.Stability and perturbation of uncountable b-frames in non-separable Hilbert spaces are studied.From the obtained results, in particular, corresponding results for tensors are derived.
We study the boundedness of the commutators of Marcinkiewicz operators µ Ω,b with rough kernels Ω ∈ Ls(S n-1 ) for some s ∈ (1, ∞] and BM O function b on generalized weighted Morrey spaces Mp,ϕ(w).In the case of b ∈ BM O(R n ) we find the sufficient conditions on the pair (ϕ 1 , ϕ 2 ) with s < p < ∞ and w ∈ A p/s or 1 < p < s and w 1-p ∈ A p /s which ensures the boundedness of the operators µ Ω,b from one generalized weighted Morrey space Mp,ϕ 1 (w) to another Mp,ϕ 2 (w).
