相关论文: On the Fountain Theorem for Continuous Functionals…

This paper is devoted to establishing results for semilinear elliptic boundary value problems where the solvability of problems subject to {\it No Flux} boundary conditions follows from the solvability of related {\it Dirichlet} boundary…

We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global…

The paper examines one-dimensional total variation flow equation with Dirichlet boundary conditions. Thanks to a new concept of "almost classical" solutions we are able to determine evolution of facets -- flat regions of solutions. A key…

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…

This paper deals with the systematic development of structure-preserving approximations for a class of nonlinear partial differential equations on networks. The class includes, for example, gas pipe network systems described by barotropic…

Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique solution for all…

New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main…

We discuss a notion of weak solution for a semilinear wave equation that models the interaction of an elastic body with a rigid substrate through an adhesive layer, relying on results in [2]. Our analysis embraces the vector-valued case in…

We adapt the precise definition of the flowing effective action in order to obtain a functional flow equation with simple properties close to physical intuition. The simplified flow equation is invariant under local gauge transformations…

We consider homogenization of Dirichlet problems for semilinear elliptic systems with non-smooth data. We suppose that the diffusion tensors H-converge if the homogenization parameter tends to zero. Our result is of implicit function…

In this paper we consider the wave equations with power type nonlinearities including time-derivatives of unknown functions and their weakly coupled systems. We propose a framework of test function method and give a simple proof of the…

This thesis presents an overview of the flow equations recently introduced by Wegner. The little known mathematical framework of the flow in the manifold of unitarily equivalent matrices, as discovered in the mathematical literature before…

In this paper, we consider a free boundary problem of a semilinear nonhomogeneous elliptic equation with Bernoulli's type free boundary. The existence and regularity of the solution to the free boundary problem are established by use of the…

We prove existence of weak solutions to the obstacle problem for semilinear wave equations (including the fractional case) by using a suitable approximating scheme in the spirit of minimizing movements. This extends the results in [9],…

The conformal mapping problem for the section of a channel filled with porous material under a rectangular dam onto the upper half-plane is considered. Similar problems arise in computing of fluid flow in hydraulic structures. As a solution…

The purpose of this paper is to study the existence of solutions for semilinear elliptic system driven by fractional Laplacian and establish some new existence results which are obtained by virtue of the local linking theorem and the saddle…

We provide a new algebraic technique to solve the sequential flow problem in polynomial space. The task is to maximise the flow through a graph where edge capacities can be changed over time by choosing a sequence of capacity labelings from…

We give a new proof of Brakke's partial regularity theorem up to C^{1,\varsigma} for weak varifold solutions of mean curvature flow by utilizing parabolic monotonicity formula, parabolic Lipschitz approximation and blow-up technique. The…

We search for non-trivial relativistic solutions of the hydrodynamic equations with quasi-inertial flows such as in the Bjorken-like models. The problem is analyzed in general and the known results are reproduced by a method proposed. A new…

In this paper, we demonstrate that potential theory provides a powerful framework for analyzing quasistationary fluid flows in bounded geometries, where the bulk dynamics are governed by elliptic equations with constant coefficients. This…