相关论文: Parabolic partial differential equations with disc…

We study the well-posedness of nonautonomous nonlinear delay equations in $\mathbb{R}^{n}$ as evolutionary equations in a proper Hilbert space. We present a construction of solving operators (nonautonomous case) or nonlinear semigroups…

In this paper we address the question of whether it is possible to integrate time-dependent high-dimensional PDEs with hierarchical tensor methods and explicit time stepping schemes. To this end, we develop sufficient conditions for…

The main objective of this work is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near stationary solutions. Such…

We consider several models of State Dependent Delay Differential Equations (SDDEs), in which the delay is affected by a small parameter. This is a very singular perturbation since the nature of the equation changes. Under some conditions,…

We study the set of $T$-periodic solutions of a class of $T$-periodically perturbed coupled and nonautonomous differential equations on manifolds. By using degree-theoretic methods we obtain a global continuation result for the $T$-periodic…

We study the second-order quasi-linear stochastic partial differential equations (SPDEs) defined on $C^1$ domains. The coefficients are random functions depending on $t,x$ and the unknown solutions. We prove the uniqueness and existence of…

We present a hybrid quantum-classical framework for solving general time-dependent parabolic partial differential equations (PDEs) using quantum variational circuits. Building on the QPINN approach, this method applies broadly to parabolic…

We further elaborate on the solvability of stochastic partial differential equations (SPDEs). We shall discuss non-autonomous partial differential equations with an abstract realization of the stochastic integral on the right-hand side. Our…

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…

In the first part we present a generalized implicit function theorem for abstract equations of the type $F(\lambda,u)=0$. We suppose that $u_0$ is a solution for $\lambda=0$ and that $F(\lambda,\cdot)$ is smooth for all $\lambda$, but,…

This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…

The paper deals with a class of cooperative functional differential equations (FDEs) with infinite delay, for which sufficient conditions for persistence and permanence are established. Here, the persistence refers to all solutions with…

We consider solutions of the Cauchy problem for semilinear equations with (possibly) different L\'evy operators. We provide various results on their convergence under the assumption that symbols of the involved operators converge to the…

In Rajeev (2013), 'Translation invariant diffusion in the space of tempered distributions', it was shown that there is an one to one correspondence between solutions of a class of finite dimensional SDEs and solutions of a class of SPDEs in…

We establish a coupled fixed points theorem for a meaningful class of mixed monotone multivalued operators and then we use it to derive some results on existence of quasisolutions and solutions to first--order functional differential…

In this paper, a class of non-Markovian forward-backward doubly stochastic systems is studied. By using the technique of functional It\^o (or path-dependent) calculus, the relationship between the systems and related path-dependent…

This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean…

We study a certain one dimensional, degenerate parabolic partial differential equation with a boundary condition which arises in pricing of Asian options. Due to degeneracy of the partial differential operator and the non-smooth boundary…

In this paper, we consider a linear heat equation with constant coefficients and a single constant delay. Such equations are commonly used to model and study various problems arising in ecology and population biology when describing the…

We consider a linear scalar delay differential equation (DDE), consisting of two arbitrary distributed time delays. We formulate necessary conditions for stability of the trivial solution which are independent of the distributions. For the…