Continuity of the Darcy's law in the low-volume fraction limit
Continuity of the fundamental operations on distributions having a specified wave front set (with a counterexample by Semyon Alesker)
The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front sets satisfy some conditions. Thus, it is natural to investigate the topological properties of these operations between spaces of distributions having a wave front set included in a given closed cone Γ of the cotangent space. As discovered by S. Alesker, the pull-back is not continuous for the usual topology on , and the tensor product is not separately continuous. In this paper,...
Continuity of the quenching time for a parabolic equation with a nonlinear boundary condition and a potential.
Continuity of the quenching time in a heat equation with a nonlinear boundary condition.
Continuity of the quenching time in a semilinear parabolic equation
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.
Continuity results for solutions of certain degenerate parabolic equations
Continuity versus nonexistence for a class of linear stochastic Cauchy problems driven by a Brownian motion
Let denote the generator of the rotation group in the space , where denotes the unit circle. We show that the stochastic Cauchy problem where is a standard Brownian motion and is fixed, has a weak solution if and only if the stochastic convolution process has a continuous modification, and that in this situation the weak solution has a continuous modification. In combination with a recent result of Brzeźniak, Peszat and Zabczyk it follows that (1) fails to have a weak solution for all...
Continuity with respect to data and parameters of weak solutions to a Stefan-like problem.
Continuous and generalized solutions of singular partial differential equations.
Continuous and estimates for the complex Monge-Ampère equation on bounded domains in .
Continuous approximation of time-periodic solutions of a linear parabolic equation
Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term
We study existence, uniqueness, continuous dependence, general decay of solutions of an initial boundary value problem for a viscoelastic wave equation with strong damping and nonlinear memory term. At first, we state and prove a theorem involving local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution with respect to the kernel function and the nonlinear terms. Finally, under suitable conditions...
Continuous dependence and stability for non linear dispersive and dissipative waves
Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem
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.
Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations.
Continuous dependence for BV-entropy solutions to strongly degenerate parabolic equations with variable coefficients
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.
Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies
In this paper, a one-dimensional Euler-Lagrange equation associated with the total variation energy, and Euler-Lagrange equations generated by approximating total variations with linear growth, are considered. Each of the problems presented can be regarded as a governing equation for steady-states in solid-liquid phase transitions. On the basis of precise structural analysis for the solutions, the continuous dependence between the solution classes of approximating problems and that of the limiting...
Continuous dependence for the Brinkman equations of flow in double-diffusive convection.
Continuous dependence for the pseudoparabolic equation.
Continuous dependence in for discontinuous solutions of the viscous -system