On the Fourier's first problem for a system of non-linear parabolic equations with unbounded coefficients
On the numerical solution of the one-dimensional convection-diffusion equation.
On the regularity of the blow-up set for semilinear heat equations
On the regularity of the weak solution of Cauchy problem for nonlinear parabolic systems via Liouville property
On the viscous Burgers equation in unbounded domain.
On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations.
On uniqueness and nonuniqueness of the positive Cauchy problem for parabolic equations with unbounded coefficients.
Optimal control for distributed systems subject to null-controllability. Application to discriminating sentinels
We consider a distributed system in which the state q is governed by a parabolic equation and a pair of controls v = (h,k) where h and k play two different roles: the control k is of controllability type while h expresses that the state q does not move too far from a given state. Therefore, it is natural to introduce the control point of view. In fact, there are several ways to state and solve optimal control problems with a pair of controls h and k, in particular the Least Squares method...
Optimal error estimates for semidiscrete phase relaxation models
Optimality conditions for state-constrained PDE control problems with time-dependent controls
Origins, analysis, numerical analysis, and numerical approximation of a forward-backward parabolic problem
Origins, analysis, numerical analysis, and numerical approximation of a forward-backward parabolic problem
We consider the analysis and numerical solution of a forward-backward boundary value problem. We provide some motivation, prove existence and uniqueness in a function class especially geared to the problem at hand, provide various energy estimates, prove a priori error estimates for the Galerkin method, and show the results of some numerical computations.
Overimplicit methods for the solution of evolution problems
Parabolic equations with coefficients depending on t and parameters
Parabolic initial-boundary value problems in Orlicz spaces
We prove some time mollification properties and imbedding results in inhomogeneous Orlicz-Sobolev spaces which allow us to solve a second order parabolic equation in Orlicz spaces.
Parabolicity of second order differential equations in Hubert space.
Parameter shifting and complete families of solutions to a singular parabolic equation
Parametrix for a characteristic Cauchy problem
Partial compactness for the 2-D Landau-Lifshitz flow.
Peano type theorem for abstract parabolic equations