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In this paper, we propose a parameter-robust preconditioner for the coupled Stokes-Darcy problem equipped with various boundary conditions, enforcing the mass conservation at the interface via a Lagrange multiplier. We rigorously establish…
In this paper we analyze a nonlinear parabolic equation characterized by a singular diffusion term describing very fast diffusion effects. The equation is settled in a smooth bounded three-dimensional domain and complemented with a general…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
Many physical problems involving heterogeneous spatial scales, such as the flow through fractured porous media, the study of fiber-reinforced materials, or the modeling of the small circulation in living tissues -- just to mention a few…
We consider a quasilinear parabolic stochastic partial differential equation driven by a multiplicative noise and study regularity properties of its weak solution satisfying classical a priori estimates. In particular, we determine…
This work is focused on the solvability of initial-boundary value problems for degenerate parabolic partial differential equations that arise in the pricing of Asian options, and on the investigation of differential and certain qualitative…
We derive the existence and uniqueness of the generalized backward doubly stochastic differential equation with sub-differential of a lower semi-continuous convex function under a non Lipschitz condition. This study allows us give a…
A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that…
We consider elliptic operators with operator-valued coefficients and discuss the associated parabolic problems. The unknowns are functions with values in a Hilbert space $W$. The system is equipped with a general class of coupled boundary…
This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…
The aim of this paper is to prove existence of weak solutions of hyperbolic-parabolic evolution inclusions defined on Lipschitz domains with mixed boundary conditions describing, for instance, damage processes and elasticity with inertia…
A boundary control problem for the pure Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved. Key words: Cahn-Hilliard equation,…
Common computational problems, such as parameter estimation in dynamic models and PDE constrained optimization, require data fitting over a set of auxiliary parameters subject to physical constraints over an underlying state. Naive…
We propose methods that augment existing numerical schemes for the simulation of hyperbolic balance laws with Dirichlet boundary conditions to allow for the simulation of a broad class of differential algebraic conditions. Our approach is…
The abstract elliptic and parabolic equations on exterior domain are considered. The equations have top-order variable coefficients. The separability properties of boundary value problems for elliptic equation and well-posedness of the…
This paper establishes the existence, uniqueness and time-space regularity of the weak solution to a nonlinear coupled parabolic system modeling temperature evolution in a coaxial heat exchanger with source terms and spatially varying…
We investigate classical solutions of nonlinear elliptic equations with two classes of dynamical boundary conditions, of reactive and reactive-diffusive type. In the latter case it is shown that well-posedness is to a large extent…
For a class of partial differential algebraic equations (PDAEs) of quasi-linear type which include nonlinear terms of convection type a possibility to determine a time and spatial index is considered. As a typical example we investigate an…
Backward stochastic partial differential equations of parabolic type with variable coefficients are considered in smooth domains. Existence and uniqueness results are given in weighted Sobolev spaces allowing the derivatives of the…
A doubly degenerate parabolic equation in non-divergent form with variable growth is investigated in this paper. In suitable spaces, we prove the existence of weak solutions of the equation for cases $1\leq m < 2$ and $m\geq 2$ in different…