Related papers: On Non-Autonomous Integro-Differential-Algebraic E…
In this paper we study maximal $L^p$-regularity for evolution equations with time-dependent operators $A$. We merely assume a measurable dependence on time. In the first part of the paper we present a new sufficient condition for the…
The evolution equations mentioned in the title of this paper read as follows: x~n = P(n)(x1; x2) , n = 1, 2 , where l is the "discrete-time" independent variable taking integer values (l =0, 1, 2, ...), xn = xn (l) are the 2 dependent…
We provide a concise introduction to the symmetry approach to integrability. Some results on integrable evolution and systems of evolution equations are reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We further…
Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with…
We prove the well-posedness of some non-linear stochastic differential equations in the sense of McKean-Vlasov driven by non-degenerate symmetric $\alpha$-stable L\'evy processes with values in $R^d$ under some mild H{\"o}lder regularity…
In this contribution, a stochastic nonlinear evolution system under Neumann boundary conditions is investigated. Precisely, we are interested in finding an existence and uniqueness result for a random heat equation coupled with a…
In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show…
Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…
We study conditions for the well-posedness of nonautonomous perturbation of evolution equations of the form \[ u'(t)=(A+B(t))u(t), \quad t \in [a,b], \] where $A$ generates a $\mathrm{C}_0$-semigroup $\left (T(t)\right )_{t\ge 0}$ with $\|…
We consider a class of elliptic variational-hemivaria\-tional inequalities in a abstract Banach space for which we introduce the concept of well-posedness in the sense of Tykhonov. We characterize the well-posedness in terms of metric…
We consider a mixed dimensional elliptic partial differential equation posed in a bulk domain with a large number of embedded interfaces. In particular, we study well-posedness of the problem and regularity of the solution. We also propose…
As mathematical model for the evolutionary equations of species the masterequation is choiced. Two formulations will be demonstrated to include the changes of parameters into the masterequation - that is, on the one hand, the formation of a…
In this paper, it is proved a very general well-posedness result for a class of constrained minimization problems.
We show that the discrete operator stemming from the time and space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines…
We provide certain compatibility conditions for m-accretive operators such that the adjoint of the sum is given by the closure of the sum of the respective adjoint. We revisit the proof of well-posedness of the abstract class of partial…
It is shown how a system of evolution equations can be developed both from the structure equations of a submanifold embedded in three-space as well as from a matrix SO(6) Lax pair. The two systems obtained this way correspond exactly when a…
The objective of the present work is to provide a well-posedness result for a capillary driven thin film equation with insoluble surfactant. The resulting parabolic system of evolution equations is not only strongly coupled and degenerated,…
We present a new method to solve in a semianalytical way the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NLO order in the x-space. The method allows to construct an evolution operator expressed in form of a rapidly…
This paper studies the well-posedness of a class of nonlocal parabolic partial differential equations (PDEs), or equivalently equilibrium Hamilton-Jacobi-Bellman equations, which has a strong tie with the characterization of the equilibrium…
The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the…