相关论文: Existence and Uniqueness of Local Solutions for a …

In this paper, we use the theory of nonlinear semigroups to establish the existence and uniqueness of both local and global solutions for a partial differential-algebraic equation (PDAE) of index one. This method is applied to a…

Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…

In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…

Abstract differential-algebraic equations (ADAEs) of a semilinear type are studied. Theorems on the existence and uniqueness of solutions and the maximal interval of existence, on the global solvability of the ADAEs, the boundedness of…

The purpose of this paper is to establish Picard-Lindel\"{o}f theorem for local uniqueness and existence results for first-order systems of nonlinear delay dynamic equations. In the linear case, we extend our results to global existence and…

In this paper, we study the well-posedness and regularity of non-autonomous stochastic differential algebraic equations (SDAEs) with nonlinear, locally Lipschitz and monotone (2) coefficients of the form (1). The main difficulty is the fact…

This paper deals with the local existence and uniqueness results for the solution of fractional differential equations with Hilfer-Hadamrd fractional derivative. Using Picard's approximations and generalizing the restrictive conditions…

A wide class of non-autonomous nonlinear parabolic partial differential equations with delay is studied. We allow in our investigations different types of delays such as constant, time-dependent, state-dependent (both discrete and…

In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone…

In this paper, we study a certain class of nonlocal partial differential equations (PDEs). The equations arise from a key problem in network science, i.e., network generation from local interaction rules, which result in a change of the…

In this paper we prove the local existence and uniqueness of solutions for a class of stochastic fractional partial differential equations driven by multiplicative noise. We also establish that for this class of equations adding linear…

In this paper we propose local and global existence results for the solution of systems characterized by the coupling of ODEs and PDEs. The coexistence of distinct mathematical formalisms represents the main feature of hybrid approaches, in…

We prove the well-posedness results, i.e. existence, uniqueness, and stability, of the solutions to a class of nonlocal fully nonlinear parabolic partial differential equations (PDEs), where there is an external time parameter $t$ on top of…

For regular and nonregular (singular) semilinear differential-algebraic equations (DAEs), we prove theorems on the existence and uniqueness of global solutions and on the blow-up of solutions, which allow one to identify the sets of initial…

In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with a nonlocal mass transfer admits the local existence of classical solutions. The equation was developed to…

We investigate the periodic and stationary solutions of distribution-dependent stochastic differential equations. While generally, the semigroups associated with the equations are nonlinear, we show that the methods of weak convergence and…

In this article, we obtain existence and uniqueness results to some problems involving complex nonlinear fractional differential equations (FDEs) in the closed unit disc of C. By help of these results, we prove that some IVPs for some…

Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDE models fail to…

The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…

In this work, we present a systematic approach to investigate the existence, multiplicity, and local gradient regularity of solutions for nonlocal quasilinear equations with local gradient degeneracy. Our method involves an interactive…