Related papers: On the Capillarity Equation in Two Dimensions

A linear constraint loop is specified by a system of linear inequalities that define the relation between the values of the program variables before and after a single execution of the loop body. In this paper we consider the problem of…

The aim of this article is to study a nonlinear system modeling a Non-Newtonian fluid of polymer aqueous solutions. We are interested here in the existence of weak solutions for the stationary problem in a bounded plane domain or in…

The paper concerns singular solutions of nonlinear elliptic equations.

The generalized Kuramoto-Sivashinsky equation in the case of the power nonlinearity with arbitrary degree is considered. New exact solutions of this equation are presented.

We report on the cited papers refs. 1 - 18 from the following points of view: What do we exactly know about solutions when no exact solution (in the sense of "solution in closed form") is available? In which sense do these solutions possess…

We discuss how the finiteness and universality of the speed of light arise in the theoretical framework introduced in [1], and derive generalized coordinate transformations, that allow to investigate physical systems in a non-classical…

We study a singular parabolic equation of the total variation type in one dimension. The problem is a simplification of the singular curvature flow. We show existence and uniqueness of weak solutions. We also prove existence of weak…

Using the framework of Colombeau algebras of generalized functions, we prove the existence and uniqueness results for global generalized solvability of semilinear hyperbolic systems with nonlinear nonlocal boundary conditions. We admit…

The hypothesis that the causal properties of space-time, as well as other properties of physical systems like unitarity, charge conservation, etc., might be decided by the higher dimensional structure (in particular, higher-dimensional…

In this paper we study a rather wide class of quasilinear parabolic problems with nonlinear boundary condition and nonstandard growth terms. It includes the important case of equations with a $p(t,x)$-Laplacian. By means of the localization…

In this paper, we investigate the global conservative solutions to the generalized Camassa-Holm equation with dual-power nonlinearities. By introducing a new set of variables, we transform the original equation into an equivalent…

This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…

We consider a certain simplification of the two-dimensional thermomicropolar fluids equations. We prove the existence of certain solutions to these equations depending on the regularity of the intial data. We investigate the uniqueness of…

We consider semilinear wave equations with small initial data in two space dimensions. For a class of wave equations with cubic nonlinearity, we show the global existence of small amplitude solutions, and give an asymptotic description of…

We prove that if a linear equation, whose coefficients are continuous rational functions on a nonsingular real algebraic surface, has a continuous solution, then it also has a continuous rational solution. This is known to fail in higher…

The aim of this article is to study the noncontrollability of the heat equation with double singular potential at an interior point and on the boundary of the domain.

In recent years, deep learning researchers have focused on how to find the interpretability behind deep learning models. However, today cognitive competence of human has not completely covered the deep learning model. In other words, there…

We give pointwise gradient bounds for solutions of (possibly non-uniformly) elliptic partial differential equations in the entire Euclidean space. The operator taken into account is very general and comprises also the singular and…

In this paper, we study the Navier-Stokes-Korteweg equations governed by the evolution of compressible fluids with capillarity effects. We first investigate the global well-posedness of solution in the critical Besov space for large initial…

We obtain a generic closed system of equations on a brane that describes its inner evolution and give a method for extending solutions on the brane to the bulk. We also discuss the cosmological implications of the closed system of equations…