Interface dynamics for an anisotropic Allen-Cahn equation
Interface model coupling via prescribed local flux balance
This paper deals with the non-conservative coupling of two one-dimensional barotropic Euler systems at an interface at x = 0. The closure pressure laws differ in the domains x < 0 and x > 0, and a Dirac source term concentrated at x = 0 models singular pressure losses. We propose two numerical methods. The first one relies on ghost state reconstructions at the interface while the second is based on a suitable relaxation framework. Both methods satisfy a well-balanced property for stationary...
Interface tracking method for compressible multifluids
This paper is concerned with numerical methods for compressible multicomponent fluids. The fluid components are assumed immiscible, and are separated by material interfaces, each endowed with its own equation of state (EOS). Cell averages of computational cells that are occupied by several fluid components require a “mixed-cell” EOS, which may not always be physically meaningful, and often leads to spurious oscillations. We present a new interface tracking algorithm, which avoids using mixed-cell...
Interfaces in solutions of diffusion-absorption equations.
We study the properties of interfaces in solutions of the Cauchy problem for the nonlinear degenerate parabolic equation ut = Δum - up in Rn x (0,T] with the parameters m > 1, p > 0 satisfying the condition m + p ≥ 2. We show that the velocity of the interface Γ(t) = ∂{supp u(x,t)} is given by the formula v = [ -m / (m-1) ∇um-1 + ∇Π ]|Γ(t) where Π is the solution of the degenerate elliptic equation div (u∇Π) + up = 0, Π = 0 on Γ(t). We give explicit formulas which represent the interface...
Interfacial dynamics for thermodynamically consistent phase-field models with nonconserved order parameter.
Interfering solutions of a nonhomogeneous Hamiltonian system.
Interior and superconvergence estimates for mixed methods for second order elliptic problems
Interior controllability of a reaction-diffusion system with cross-diffusion matrix.
Interior controllability of a broad class of reaction diffusion equations.
Interior differentiability of weak solutions to parabolic systems with quadratic growth nonlinearities
Interior error estimates for semi-discrete Galerkin approximations for parabolic equations
Interior error estimates of projection methods
Interior estimates for solutions of Abreu's equation.
This paper develops various estimates for solutions of a nonlinear, fouth order PDE which corresponds to prescribing the scalar curvature of a toric Kähler metric. The results combine techniques from Riemannian geometry and from the theory of Monge-Ampère equations.
Interior estimates for some semilinear elliptic problem with critical nonlinearity
Interior estimates in the theory of partial differential equations and their application to initial value problems.
Interior feedback stabilization of wave equations with time dependent delay.
Interior gradient estimates for nonuniformly parabolic equations. II.
Interior Hölder estimates for solutions of Schrödinger equations and the regularity of nodal sets
Interior penalty discontinuous approximations of elliptic problems.
Interior point control and observation for the wave equation.