相关论文: On the Capillarity Equation in Two Dimensions

We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…

We study the behaviour near a boundary point a of any positive solution of a nonlinear elliptic equations with forcing term which vanishes on the boundary except at a. Our results are based upon a priori estimates for solutions and…

We investigate the global existence and long-time behavior of large solutions, in the high-capillarity regime, for a general multidimensional non-conservative compressible two-fluid model with the capillary pressure relation…

We investigate the behavior of the solutions of the ray equation in isotropic media. We discuss local and global transversals and wavefronts and give examples of rays without wavefronts.

In this paper, we discuss singular Neumann boundary problem for a class of nonlinear parabolic equations in one space dimension. Our boundary problem describes motion of a planar curve sliding along the boundary with a zero contact angle,…

We study the existence of nontrivial weak solutions for a class of generalized $p(x)$-biharmonic equations with singular nonlinearity and Navier boundary condition. The proofs combine variational and topological arguments. The approach…

We investigate the Cauchy-Dirichlet problem for linear parabolic equations in divergence form. Under mild assumptions on the source term and the domain, we prove the existence of globally H\"{o}lder continuous solutions. Notably, our…

We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…

We recall the classical theory of capillarity, describing the shape of a liquid droplet in a container, and present a recent approach which aims at accounting for long-range particle interactions. This nonlocal setting recovers the…

The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…

The Plateau's problem seeks to determine a surface of minimal area which spans a given boundary. It is widely studied for its varied mathematical formulations, applications and relevance to physical models such as soap films. We revisit the…

Although much research has been devoted to extremal problems on non-overlapping domains little is known about all solutions of this problems. We generalized some of this problems on the case of more general systems of points. It was solved…

In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…

We research the natural causality of the Universe. We find that the equation of causality provides very good results on physics. That is our first endeavour and success in describing a quantitative expression of the law of causality. Hence,…

The aim of this work is studding the behavior of solutions of initial boundary problem for degenerated nonlinear parabolic equation of the second order, conditions of existence and non-existence in whole by time solutions, is establish.

We consider the Dirichlet problem for a class of semilinear equations on two dimensional convex domains. We give a sufficient condition for the solution to be concave. Our condition uses comparison with ellipses, and is motivated by an idea…

Partial descriptions of the Universe are presented in the form of linear equations considered in the free (full, super) Fock space. The universal properties of these equations are discussed. The closure problem caused by computational and…

This work is devoted to prove existence of global weak solutions for a general isothermal model of capillary fluids derived by J.- E Dunn and J. Serrin (1985) [6], which can be used as a phase transition model. We improve the results of [5]…

We consider nonlinear elliptic equations which contains global coupling as a nonlinear term. We classify the existence of all possible positive solutions to this problem.

The Dirac equation is solved for a pseudoscalar Coulomb potential in a two-dimensional world. An infinite sequence of bounded solutions are obtained. These results are in sharp contrast with those ones obtained in 3+1 dimensions where no…