On the backward parabolic equation: a critical survey of some current methods
On the base and the essential base in parabolic potential theory
On the behavior of solutions of parbolic equations with unbounded coefficients
On the blowup of multidimensional semilinear heat equations
On the boundary convergence of solutions to the Hermite-Schrödinger equation
In the half-space , consider the Hermite-Schrödinger equation i∂u/∂t = -Δu + |x|²u, with given boundary values on . We prove a formula that links the solution of this problem to that of the classical Schrödinger equation. It shows that mixed norm estimates for the Hermite-Schrödinger equation can be obtained immediately from those known in the classical case. In one space dimension, we deduce sharp pointwise convergence results at the boundary by means of this link.
On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions
On the boundary value problem for the spectrally loaded heat conduction operator.
On the boundness of the Stokes semigroup in two-dimensional exterior domains.
On the Caginalp system with dynamic boundary conditions and singular potentials
This article is devoted to the study of the Caginalp phase field system with dynamic boundary conditions and singular potentials. We first show that, for initial data in , the solutions are strictly separated from the singularities of the potential. This turns out to be our main argument in the proof of the existence and uniqueness of solutions. We then prove the existence of global attractors. In the last part of the article, we adapt well-known results concerning the Łojasiewicz inequality in...
On the Cauchy problem and initial traces for a class of evolution equations with strongly nonlinear sources
On the Cauchy problem for a class of parabolic equations with variable density
The well-posedness of the Cauchy problem for a class of parabolic equations with variable density is investigated. Necessary and sufficient conditions for existence and uniqueness in the class of bounded solutions are proved. If these conditions fail, sufficient conditions are given to ensure well-posedness in the class of bounded solutions which satisfy suitable constraints at infinity.
On the Cauchy problem for a degenerate parabolic differential equation.
On the Cauchy problem for a second order semilinear parabolic equation with factored linear part.
On the Cauchy problem for the equation of one-dimensional non-stationary filtration with non-continuous initial data
On the Cauchy problem of a quasilinear degenerate parabolic equation.
On the Chebyshev penalty method for parabolic and hyperbolic equations
On the continuity of heat potentials
On the Convective Cahn-Hilliard Equation
The author studies the convective Cahn-Hilliard equation. Some results on the existence of classical solutions and asymptotic behavior of solutions are established. The instability of the traveling waves is also discussed.
On the convergence of a factorized vector finite difference scheme.
On the convergence of a multicomponent alternating direction difference scheme.