Construction of Green's functions for the Black-Scholes equation.
Contact problems with given time-dependent friction force in linear viscoelasticity
Continuability in time of smooth solutions of strong-nonlinear nondiagonal parabolic systems
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 is studied. Smooth extendibility of the solution up to is proved, provided that “normilized local energies” of the solution are uniformly bounded on . For the case where determines the maximal interval...
Continuation of the connection matrix for singularly perturbed hyperbolic equations
Continuity for bounded solutions of multiphase Stefan problem
We establish the continuity of bounded local solutions of the equation . Here is any coercive maximal monotone graph in , 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.
Continuity of attractors for a reaction-diffusion problem with respect to variations of the domain.
Continuity of solutions of the porous media equation
Continuity of the quenching time for a parabolic equation with a nonlinear boundary condition and a potential.
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 with respect to data and parameters of weak solutions to a Stefan-like problem.
Continuous approximation of time-periodic solutions of a linear parabolic equation
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 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 the Brinkman equations of flow in double-diffusive convection.
Continuous dependence for the pseudoparabolic equation.
Continuous dependence of solutions to mixed boundary value problems for a parabolic equation.
Continuous dependence of the entropy solution of general parabolic equation
We consider the general parabolic equation : in with
Continuous dependence on modeling for some well-posed perturbations of the backward heat equation.
Continuous host-macroparasite models with application to aquaculture.