In this manuscript, we will study the asymptotic behavior for a class of nonlocal diffusion equations associated with weighted fractional $$\wp (\cdot )$$ -Laplacian operator involving constant/variable exponent, ^{-}:=\min _{(x,y) \in {\overline{\Omega }}\times }}} \wp (x,y)\geqslant \max \left\{ 2N/(N+2s),1\right\} $$ and $$s\in (0,1).$$ case constant exponents, under some appropriate conditi...

‎in this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎to this end‎, ‎we aim to replace the field of scalars $ mathbb{r} $ by self-adjoint elements of a commutative $ c^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎first‎, ‎we put forward the concept of operator-valued tensors and extend semi-riemannian...

Abstract. Let X be a UMD space with type t and cotype q, and let Tm be a Fourier multiplier operator with a scalar-valued symbol m. If |∂m(ξ)| . |ξ|−|α| for all |α| ≤ ⌊n/max(t, q′)⌋ + 1, then Tm is bounded on L(R;X) for all p ∈ (1,∞). For scalar-valued multipliers, this improves the theorem of Girardi and Weis (J. Funct. Anal., 2003) who required similar assumptions for derivatives up to the or...

We present the salient features of a min-max game theory developed in the context of coupled PDE's with an interface. Canonical applications include linear fluid-structure interaction problem modeled by Oseen's equations coupled with elastic waves. We shall consider two models for the structures: elastic and visco-elastic. Control and disturbance are allowed to act at the interface between the ...

In this project, we consider minimizing multiple linear objective functions under a max-t-norm fuzzy relational equation constraint. Since the feasible domain of a max-Archimedean t-norm relational equation constraint is generally nonconvex, traditionally mathematical programming techiniques may have difficulty in yielding efficient solutions for such problems. In this paper, we apply the two-p...