相关论文: On weak solutions for fourth-order problems involv…

We derive an explicit formula for global weak solutions of the one dimensional system of pressure-less Euler-Poisson equations. Our variational formulation is an extension of the well-known formula for entropy solutions of the scalar…

We prove existence of weak solutions for the fully inhomogeneous, stationary generalized Navier-Stokes equations for shear-thinning fluids. Our proof is based on the theory of pseudomonotone operators and the Lipschitz truncation method,…

This article deals with the study of the following Kirchhoff equation with exponential nonlinearity of Choquard type (see $(KC)$ below). We use the variational method in the light of Moser-Trudinger inequality to show the existence of weak…

In this paper, we present a posteriori error estimation for weak Galerkin method applied to fourth order singularly perturbed problem. The weak Galerkin discretization space and numerical scheme are first described. A fully computable…

We discuss the role of weakly normal formulas in the theory of thorn forking, as part of a commentary on the paper "Thorn forking and stable forking" by Ealy and Onshuus (Rev. acad. colomb. cienc. exact. fis. nat. vol.40 no.157 Bogot\'a…

This paper focuses on integrating the networks and adversarial training into constrained optimization problems to develop a framework algorithm for constrained optimization problems. For such problems, we first transform them into minimax…

The notion of weak cyclic monotonicity of set-valued maps generalizing the cyclic monotonicity is introduced. The existence of solutions of differential inclusions with compact, upper semi-continuous, not necessarily convex right-hand sides…

This paper deals with the existence of solutions to a class of fourth order nonlinear elliptic equations. The technique used relies on critical points theory. The solutions appeared as critical points of a functional restricted to a…

By applying Mountain Pass Lemma, Ekeland's and Ricceri's variational principle, Fountain Theorem, we prove the existence and multiplicity of solutions for the following Robin problem \begin{equation*} \left\{ \begin{array}{cc}…

We are concerned with the existence of global in time solutions to the Cauchy problem for semi-linear Klein-Gordon equations with memory-type dissipation in $\mathbb{R}^n$. In the first place, we consider the linearized equation: applying…

The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…

In this paper, we introduce Hardy spaces with variable exponents defined on a probability space and develop the martingale theory of variable Hardy spaces. We prove the weak type and strong type inequalities on Doob's maximal operator and…

We deal with the existence of weak solutions for a mixed Neumann-Robin-Cauchy problem. The existence results are based on global-in-time estimates of approximating solutions, and the passage to the limit exploits compactness techniques. We…

This thesis pertains to the study of elliptic and parabolic partial differential equations on "thin" structures. The first main objective is to establish the strong and weak low-dimensional counterparts of the parabolic Neumann problem. The…

In this paper we study existence and spectral properties for weak solutions of Neumann and Dirichlet problems associated to second order linear degenerate elliptic partial differential operators $X$, with rough coefficients of the form…

We consider the Cauchy problem of third order Benjamin-Ono type equations on the torus. Nonlinear terms may yield derivative losses, which prevents us from using the classical energy method. In order to overcome that difficulty, we add a…

Here, we consider stationary monotone mean-field games (MFGs) and study the existence of weak solutions. First, we introduce a regularized problem that preserves the monotonicity. Next, using variational inequalities techniques, we prove…

The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…

In this short note, we present some new existence results for a nonlinear fourth-order two-point boundary value problem with integral condition. The existence results are obtained by using the Leray-Schauder fixed point theorem. Our work…

We show that in the presence of massive particles such as nucleons, the standard low energy expansion in powers of meson momenta and light quark masses in general only converges in part of the low energy region. The expansion of the scalar…