Discontinuous parabolic problems with a nonlocal initial condition.
Discrete maximum principle in parabolic boundary-value problems
Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2d applications
Our studies are motivated by a desire to model long-time simulations of possible scenarios for a waste disposal. Numerical methods are developed for solving the arising systems of convection-diffusion-dispersion-reaction equations, and the received results of several discretization methods are presented. We concentrate on linear reaction systems, which can be solved analytically. In the numerical methods, we use large time-steps to achieve long simulation times of about 10 000 years. We propose...
Distribution-valued weak solutions to a parabolic problem arising in financial mathematics.
Dynamique des tourbillons de vorticité pour l’équation de Ginzburg-Landau parabolique
Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
In this paper, we extend the reduced-basis approximations developed earlier for linear elliptic and parabolic partial differential equations with affine parameter dependence to problems involving (a) nonaffine dependence on the parameter, and (b) nonlinear dependence on the field variable. The method replaces the nonaffine and nonlinear terms with a coefficient function approximation which then permits an efficient offline-online computational decomposition. We first review the coefficient function...
Eine parabolische Gleichung mit vergänglichen Lösungen.
Einschliessungsaussagen bei Systemen semilinearer parabolischer Differentialgleichungen
Für die Lösungen seminlinearer parabolischer Differentialgleichungen werden Einschliessungsaussagen hergeleitet. Hierbei werden Aussagen zur Stabilität von Lösungen ermittelt. Die Resultate werden am Beispiel der Fitzhugh-Nagumo Gleichungen diskutiert.
Ergodic properties of multidimensional Brownian motion with rebirth.
Error control and adaptivity for a phase relaxation model
Error Control and Andaptivity for a Phase Relaxation Model
The phase relaxation model is a diffuse interface model with small parameter ε which consists of a parabolic PDE for temperature θ and an ODE with double obstacles for phase variable χ. To decouple the system a semi-explicit Euler method with variable step-size τ is used for time discretization, which requires the stability constraint τ ≤ ε. Conforming piecewise linear finite elements over highly graded simplicial meshes with parameter h are further employed for space discretization. A posteriori...
Estimates for the maximum modulus of solutions to the Burgers system of equations.
Estimation of a temporally and spatially varying diffusion coefficinet in a parabolic system by an augmented Lagrangian technique.
Estimations uniformes à l’explosion pour les équations de la chaleur non linéaires et applications
Euclid΄s algorithm and accelerated iterative methods
Existence and asymptotics of solutions of the Debye-Nernst-Planck system in ℝ²
We investigate a system describing electrically charged particles in the whole space ℝ². Our main goal is to describe large time behavior of solutions which start their evolution from initial data of small size. This is achieved using radially symmetric self-similar solutions.
Existence and nonexistence of global solutions of the quasilinear parabolic equations with inhomogeneous terms.
Existence and nonexistence results for a class of linear and semilinear parabolic equations related to some Caffarelli-Kohn-Nirenberg inequalities
In this work we study the problem in , in , on , in , is a bounded regular domain such that , , , , and are positive functions such...
Existence of global attractors in for -Laplacian parabolic equation in .
Existence of multiple solutions for a nonlinearly perturbed elliptic parabolic system in .