The parallel space-time adaptivity techniques for solving a cancer invasion model are
investigated in the present work. Mathematically, the model comprises three coupled …

The solution of time fractional partial differential equations in general exhibit a weak
singularity near the initial time. In this article we propose a method for solving time fractional …

In this paper, the virtual element method is employed to approximate semilinear elliptic
problems over arbitrary polygonal meshes. The nonlinear load term is approximated by …

In this paper, we study a time‐fractional initial‐boundary value problem of Kirchhoff type
involving memory term for non‐homogeneous materials. As a consequence of energy …

In this article, we study the semi discrete and fully discrete formulations for a Kirchhoff type
quasilinear integro-differential equation (D α) involving time-fractional derivative of order …

We study motility-induced phase separation (MIPS) in living active matter, in which cells
interact through chemical signaling, or quorum sensing. In contrast to previous theories of …

In this article, we have considered a nonlinear nonlocal time dependent fourth order
equation demonstrating the deformation of a thin and narrow rectangular plate. We propose …

In this paper, we consider an optimal control problem governed by a kind of Kirchhoff-type
equation, which plays an important role in the phenomenon of beam vibration. Firstly, the …

Nonlocal problems involving fourth-order terms pose several difficulties such as numerical
discretization and its related convergences analysis. In this paper, the well-posedness of the …

This article establishes the existence of a fully discrete weak solution for the tumor growth
model, which is described by a coupled non-linear reaction-diffusion system. This model …