A class of quasilinear parabolic systems with quadratic nonlinearities in the gradient is considered. It is assumed that the elliptic operator of a system has variational structure. In the multidimensional case, the behavior of solutions of the Cauchy-Dirichlet problem smooth on a time interval $[0,T)$ is studied. Smooth extendibility of the solution up to $t=T$ is proved, provided that “normilized local energies” of the solution are uniformly bounded on $[0,T)$. For the case where $[0,T)$ determines the maximal interval...

We establish the continuity of bounded local solutions of the equation $\beta {\left(u\right)}_t=\mathrm{\Delta }u$. Here $\beta$ is any coercive maximal monotone graph in $\mathbb{R}\times \mathbb{R}$, bounded for bounded values of its argument. The multiphase Stefan problem and the Buckley-Leverett model of two immiscible fluids in a porous medium give rise to such singular equations.

In this paper, we consider the following initial-boundary value problem [...] where Ω is a bounded domain in RN with smooth boundary ∂Ω, p > 0, Δ is the Laplacian, v is the exterior normal unit vector on ∂Ω. Under some assumptions, we show that the solution of the above problem quenches in a finite time and estimate its quenching time. We also prove the continuity of the quenching time as a function of the initial data u0. Finally, we give some numerical results to illustrate our analysis.

This paper concerns continuous dependence estimates for Hamilton-Jacobi-Bellman-Isaacs operators. We establish such an estimate for the parabolic Cauchy problem in the whole space  [0, +∞) × ℝn and, under some periodicity and either ellipticity or controllability assumptions, we deduce a similar estimate for the ergodic constant associated to the operator. An interesting byproduct of the latter result will be the local uniform convergence for some classes of singular perturbation problems.

We consider the Cauchy problem for degenerate parabolic equations with variable coefficients. The equation has nonlinear convective term and degenerate diffusion term which depends on the spatial and time variables. In this paper, we prove the continuous dependence for entropy solutions in the space BV to the problem not only initial function but also all coefficients.

We consider the general parabolic equation :$u_t-\Delta b\left(u\right)+divF\left(u\right)=f$ in $Q=]0,T[\times {ℝ}^N,T\>0$ with ${\displaystyle u_0\in L^{\infty }\left({ℝ}^N\right),}$$ for a .... Continuous dependence on modeling for some well-posed perturbations of the backward heat equation. Ames, K.A., Payne, L.E. (1999) Journal of Inequalities and Applications [electronic only] Continuous host-macroparasite models with application to aquaculture. Marquet, Catherine Bouloux (2004) Electronic Journal of Differential Equations (EJDE) [electronic only] Contractivity of Locally One-Dimensional Splitting Methods. J.G. Verwer (1984) Numerische Mathematik Currently displaying 81 – 100 of 178 Previous Page 5 Next $