Sweta Tiwari

Bio: Sweta Tiwari is an academic researcher from Indian Institute of Technology Guwahati. The author has contributed to research in topics: Bounded function & Type (model theory). The author has an hindex of 4, co-authored 16 publications receiving 67 citations. Previous affiliations of Sweta Tiwari include National Autonomous University of Mexico & Tata Institute of Fundamental Research.

Variable order nonlocal Choquard problem with variable exponents

Abstract: In this article, we study the existence/multiplicity results for the variable order nonlocal Choquard problem with variable exponents (−Δ)p(⋅)s(⋅)u(x)=λ|u(x)|α(x)−2u(x)+∫ΩF(y,u(y))|x−y|μ(x,y)dyf(x,...

Quasilinear parabolic problem with p ( x )-laplacian: existence, uniqueness of weak solutions and stabilization

Abstract: We discuss the existence and uniqueness of the weak solution of the following quasilinear parabolic equation $$ \left\{ \begin{array}{ll} u_t-\Delta _{p(x)}u = f(x,u)&\quad \text{in } \quad Q_T \stackrel{{\rm{def}}}{=} (0,T)\times\Omega,\\ u = 0 & \quad\text{on} \quad \Sigma_T\stackrel{{\rm{def}}}{=} (0,T)\times\partial\Omega,\\ u(0,x)=u_0(x)& \quad \text{in} \quad \Omega \end{array} \right. \quad\quad (P_{T}) $$ involving the p(x)-laplacian operator. Next, we discuss the global behaviour of solutions and in particular some stabilization properties.

Variable order nonlocal Choquard problem with variable exponents

Abstract: In this article, we study the existence/multiplicity results for the following variable order nonlocal Choquard problem with variable exponents (-\Delta)_{p(\cdot)}^{s(\cdot)}u(x)&=\lambda|u(x)|^{\alpha(x)-2}u(x)+ \left(\DD\int_\Omega\frac{F(y,u(y))}{|x-y|^{\mu(x,y)}}dy\right)f(x,u(x)), x\in \Omega, u(x)&=0, x\in \mathbb R^N\setminus\Omega, where $\Omega\subset\mathbb R^N$ is a smooth and bounded domain, $N\geq 2$, $p,s,\mu$ and $\alpha$ are continuous functions on $\mathbb R^N\times\mathbb R^N$ and $f(x,t)$ is Carathedory function. Under suitable assumption on $s,p,\mu,\alpha$ and $f(x,t)$, first we study the analogous Hardy-Sobolev-Littlewood-type result for variable exponents suitable for the fractional Sobolev space with variable order and variable exponents. Then we give the existence/multiplicity results for the above equation.

Elliptic Problems in with Critical and Singular Discontinuous Nonlinearities

Abstract: Let be a bounded domain in , with smooth boundary, and be real numbers. Define and the characteristic function of a set A by . We consider the following critical problem with singular and discontinuous nonlinearity:We study the existence and the global multiplicity of solutions to the above problem.

Quasilinear parabolic problem with $p(x)$-Laplacian: existence, uniqueness of weak solutions and stabilization

Abstract: We discuss the existence and uniqueness of the weak solution of the following quasilinear parabolic equation $u_t-\Delta _{p(x)}u = f(x,u)$ in $ (0,T)\times\Omega$; $u = 0$ on $(0,T)\times\partial\Omega$; $u(0,x)=u_0(x)$ in $\Omega$; involving the $p(x)$-Laplacian operator. Next, we discuss the global behaviour of solutions and in particular some stabilization properties.

Positive solutions of fractional elliptic equation with critical and singular nonlinearity

Abstract: Abstract In this article, we study the following fractional elliptic equation with critical growth and singular nonlinearity: ( - Δ ) s ⁢ u = u - q + λ ⁢ u 2 s * - 1 , u > 0 in ⁢ Ω , u = 0 in ⁢ ℝ n ∖ Ω , (-\\Delta)^{s}u=u^{-q}+\\lambda u^{{2^{*}_{s}}-1},\\qquad u>0\\quad\\text{in }% \\Omega,\\qquad u=0\\quad\\text{in }\\mathbb{R}^{n}\\setminus\\Omega, where Ω is a bounded domain in ℝ n {\\mathbb{R}^{n}} with smooth boundary ∂ ⁡ Ω {\\partial\\Omega} , n > 2 ⁢ s {n>2s} , s ∈ ( 0 , 1 ) {s\\in(0,1)} , λ > 0 {\\lambda>0} , q > 0 {q>0} and 2 s * = 2 ⁢ n n - 2 ⁢ s {2^{*}_{s}=\\frac{2n}{n-2s}} . We use variational methods to show the existence and multiplicity of positive solutions with respect to the parameter λ.

Variable order nonlocal Choquard problem with variable exponents

Abstract: In this article, we study the existence/multiplicity results for the variable order nonlocal Choquard problem with variable exponents (−Δ)p(⋅)s(⋅)u(x)=λ|u(x)|α(x)−2u(x)+∫ΩF(y,u(y))|x−y|μ(x,y)dyf(x,...

Quasilinear parabolic problem with variable exponent: Qualitative analysis and stabilization

Abstract: We discuss the existence and uniqueness of the weak solution of the following nonlinear parabolic problem: (PT) ut −∇⋅a(x,∇u) = f(x,u)in QT=def(0,T) × Ω,u = 0 on ΣT=def(0,T) × ∂Ω,u(0,x) = u0(x) in Ω, which involves a quasilinear elliptic operator of Leray–Lions type with variable exponents. Next, we discuss the global behavior of solutions and in particular the convergence to a stationary solution as t →∞.