We consider the following chemotaxis-growth system, featuring density-suppressed motility and a $\theta$-logistic growth term that incorporates a strong Allee effect: \begin{equation*} \left\{ \begin{aligned} u_t&= \Delta(\gamma(v)u) + \mu u(1-u^\theta)(u-A),&x \in \Omega, \quad t>0, v_t&= \Delta v - v+ w^\beta,&x \in...
O. Tripathi, Sourav Kumar Sasmal, Manil T. Mohan· 0 citations
We study the Kuramoto--Sivashinsky (KS) equation in one, two, and three spatial dimensions subject to a codimension-one constraint. The constraint preserves the \(L^2\)-norm of the solution and consequently provides a uniform a priori bound that plays a central role in the higher-order energy estimates. In one spatial...
This work is devoted to the infinite-dimensional second-order Hamilton-Jacobi-Bellman equation associated, via the dynamic programming approach, with an optimal control problem for the two- and three-dimensional stochastic convective Brinkman-Forchheimer equations on the torus, driven by an additive Hilbert space value...
Sagar Gautam, Manil T. Mohan· Communications in Contempora...· 0 citations
We construct divergence-free, vector-valued approximation functions on the whole space $\mathbb{R}^d$, $d\geq 2$, as well as on general unbounded domains of uniform $\mathrm{C}^{1,1}$-type. These approximations converge simultaneously in both Sobolev and Lebesgue spaces. In the whole-space setting, we employ Bogovski\u...
Akram Khan, Sagar Gautam, Manil T. Mohan· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
