相关论文: On the Capillarity Equation in Two Dimensions

We establish the boundedness character of solutions of a system of rational difference equations with a variable coefficient

We study a boundary-value quasilinear elliptic problem on a generic time scale. Making use of the fixed-point index theory, sufficient conditions are given to obtain existence, multiplicity, and infinite solvability of positive solutions.

This paper is concerned with the convergence of the solution of general elliptic boundary value problems in cylindrical domain, when some directions of the domain go to infinity.

A combination of some weighted energy estimates is applied for the Cauchy problem of quasilinear wave equations with the standard null conditions in three spatial dimensions. Alternative proofs for global solutions are shown including the…

We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearities are maximal monotone graphs, without restrictions on the…

We report on some recent existence and uniqueness results for elliptic equations subject to Dirichlet boundary condition and involving a singular nonlinearity. We take into account the following types of problems: (i) singular problems with…

We obtain sufficient conditions for the uniqueness of solutions to the Cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous.

A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…

This work is devoted to the study of the initial boundary value problem for a general non isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985), which can be used as a phase transition model. We distinguish two cases,…

We consider a semilinear parabolic equation with flux at the boundary governed by a nonlinear memory. We give some conditions for this problem which guarantee global existence of solutions as well as blow up in finite time of all nontrivial…

A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…

We study a fractional diffusion problem in the divergence form in one space dimension. We define a notion of the viscosity solution. We prove existence of viscosity solutions to the fractional diffusion problem with the Dirichlet boundary…

This paper concerns a study of the pointwise behaviour of positive solutions to certain quasi-linear elliptic equations with natural growth terms, under minimal regularity assumptions on the underlying coefficients. Our primary results…

In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…

The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…

We consider variational problems with regular H{\"o}lderian weight or boundary singularity, and Dirichlet condition. We prove the boundedness of the volume of the solutions to these equations on analytic domains.

The goal of this article is to discuss a recent conjecture of the two authors, which aims to describe the long time behavior of solutions to one-dimensional dispersive equations with cubic and higher nonlinearities. These problems arguably…

We prove the global uniqueness in determination of the conductivity, the permeability and the permittivity of two dimensional Maxwell's equations by partial Dirichlet-to-Neumann map limited to an arbitrary subboundary.

In this paper, we show that the global solution of the surface anisotropic two-dimensional quasi-geostrophic equation with fractional horizontal dissipation and vertical thermal diffusion established by the author in [2] is bounded in…

We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…