Related papers: Local boundedness and higher integrability for the…
This manuscript presents a new extended linear system for integral equation based techniques for solving boundary value problems on locally perturbed geometries. The new extended linear system is similar to a previously presented technique…
We have established previously, in a lead-in study, that the spreading of liquids in particulate porous media at low saturation levels, characteristically less than 10% of the void space, has very distinctive features in comparison to that…
We introduce middle convolution for systems of linear differential equations with irregular singular points, and we presend a tentative definition of the index of rigidity for them. Under some assumption, we show a list of terminal patterns…
We prove the global existence of finite energy weak solutions to the general liquid crystals system. The problem is studied in bounded domain of $R^3$ with Dirichlet boundary conditions and the whole space $R^3$.
We investigate the existence and multiplicity of solutions for higher order discrete boundary value problems via critical point theory.
We consider parabolic systems with nonlinear dynamic boundary conditions, for which we give a rigorous derivation. Then, we give them several physical interpretations which includes an interpretation for the porous-medium equation, and for…
This paper is concerned with relationships of weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems. It is shown that weakly mixing implies topologically weakly mixing and sensitivity for measurable…
This work is concerned with both higher integrability and differentiability for linear nonlocal equations with possibly very irregular coefficients of VMO-type or even coefficients that are merely small in BMO. In particular, such…
We study the weak solutions to the electron-MHD system and obtain a conditional uniqueness result. In addition, we prove conservation of helicity for weak solutions to the electron-MHD system under a geometric condition.
We investigate existence and uniqueness of weak solutions of the Cauchy problem for the porous medium equation on negatively curved Riemannian manifolds. We show existence of solutions taking as initial condition a finite Radon measure, not…
We study the weak solvability of a nonlinearly coupled system of parabolic and pseudo-parabolic equations describing the interplay between mechanics, chemical reactions, diffusion and flow in a mixture theory framework. Our approach relies…
We introduce the notion of relative entropy for the weak solutions of the compressible Navier-Stokes system. We show that any finite energy weak solution satisfies a relative entropy inequality for any pair of sufficiently smooth test…
We introduce and study minimal (with respect to inclusion) solutions of systems of tropical linear differential equations. We describe the set of all minimal solutions for a single equation. It is shown that any tropical linear differential…
Several older and more recent results on the boundaries of solvability and unsolvability in tag systems are surveyed. Emphasis will be put on the significance of computer experiments in research on very small tag systems.
Regularity estimates in time and space for solutions to the porous medium equation are shown in the scale of Sobolev spaces. In addition, higher spatial regularity for powers of the solutions is obtained. Scaling arguments indicate that…
In this study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface…
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…
In this paper we study qualitative properties of initial traces of solutions to the porous medium equation with power nonlinearity, and obtain necessary conditions for the existence of solutions to the corresponding Cauchy problem.…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…
In this paper, we analyze the existence of solution for a fractional elliptic system coupled by critical nonlinearities and endowed with mixed Dirichlet-Neumann boundary conditions. By means of variational methods and an…