Abstract A one–spatial dimensional tumour growth model Breward et al. ( 2001, 2002, 2003) that consists of three dependent variables space and time is considered. These are volume fraction cells, velocity nutrient concentration. The satisfy a coupled system semilinear advection equation (hyperbolic), simplified linear Stokes (elliptic), diffusion (parabolic) with appropriate conditions on the t...

This work is concerned with the the stability analysis of the constant stationary solution of the following fully nonlinear parabolic equation: ut+ 1 2u 2 x = f(cuuxx)+lnu, x ∈ (0, l) with ux(0, t) = ux(l, t) = 0, where f is a smooth function satisfying f(0) = 0, f ′ > 0 and f(IR) = IR. In the case where f(s) = ln [ exp(s)−1 s ] , this equation represents the evolution of the perturbations of t...

In this contribution, we provide answers to the following two questions: 1) Which semilinear parabolic equations are approximately controllable (in the L sense) ? 2) Which are null controllable ? 74 ESAIM: Proc., Vol. 4, 1998, 73-81

In this paper, we study the blowup rate estimate for a system of semilinear parabolic equations. The blowup rate depends on whether the two components of the solution of this system blow up simultaneously or not.

We find a bound for the modulus of continuity of the blow-up time for the semilinear parabolic problem ut = ∆u + |u|u, with respect to the initial data.

Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In ...