An initial boundary value problem for Maxwell's equations in a parabolic limit case.
An initial-boundary value problem for quasi-linear parabolic systems of higher order
An Initial-Boundary-Value Problem for a Certain Density-Dependent Diffusion System.
An instantaneous semi-Lagrangian approach for boundary control of a melting problem
In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on the characteristics method. The resulting time independent control problems are formulated as function space optimization problems with complementarity constraints. At each time step, the existence of an optimal solution is proved and first-order optimality conditions...
An integral equation technique for solving mixed boundary value problems
An integral estimate for weak solutions to some quasilinear elliptic systems
We prove an integral estimate for weak solutions to some quasilinear elliptic systems; such an estimate provides us with the following regularity result: weak solutions are bounded.
An integral formula for the derivatives of solutions of certain elliptic systems
An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid
The Dirac equation for spinor-valued fields on the Minkowski space of even dimension form a hyperbolic system of partial differential equations. In the paper, we are showing how to reconstruct the solution from initial data given on the upper sheet of the hyperboloid. In particular, we derive an integral formula expressing the value of in a chosen point as an integral over a compact cycle given by the intersection of the null cone with in the Minkowski space .
An integral geometry problem along geodesics and a computational approach.
An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems
In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finitedimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance,...
An integro-differential inequality related to the smallest positive eigenvalue ofp(x)-Laplacian Dirichlet problem
We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.
An interacting particles process for Burgers equation on the circle.
An interpolation inequality in exterior domains
An interpretation of the Vakulenko-Kapitanskiĭ estimate.
An introduction to probabilistic methods with applications
This special volume of the ESAIM Journal, Mathematical Modelling and Numerical Analysis, contains a collection of articles on probabilistic interpretations of some classes of nonlinear integro-differential equations. The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis, with applications in a variety of scientific disciplines, including physics, biology, fluid mechanics, molecular chemistry, financial mathematics and bayesian statistics....
An introduction to the Einstein-Vlasov system
An invariance method for constructing fundamental solutions for
An inverse boundary-value problem for semilinear elliptic equations.
An inverse eigenvalue problem for an arbitrary multiply connected bounded region in .
An inverse eigenvalue problem for an arbitrary multiply connected bounded region: An extension to higher dimensions.