Balls and Quasi-Metrics: A Space of Homogenous Type Modeling the Real Analysis Related to the Monge-Ampère Equation.
Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type
We establish the existence, uniqueness and main properties of the fundamental solutions for the fractional porous medium equation introduced in [51]. They are self-similar functions of the form with suitable and . As a main application of this construction, we prove that the asymptotic behaviour of general solutions is represented by such special solutions. Very singular solutions are also constructed. Among other interesting qualitative properties of the equation we prove an Aleksandrov reflection...
Baroclinic Kelvin Waves in a Rotating Circular Basin
A linear, uniformly stratified ocean model is used to investigate propagation of baroclinic Kelvin waves in a cylindrical basin. It is found that smaller wave amplitudes are inherent to higher mode individual terms of the obtained solutions that are also evanescent away of a costal line toward the center of the circular basin. It is also shown that the individual terms if the obtained solutions can be visualized as spinning patterns in rotating stratified fluid confined in a circular basin. Moreover,...
Barriers on cones for degenerate quasilinear elliptic operators.
Basic boundary value problems of thermoelasticity for anisotropic bodies with cuts. I.
Basic boundary value problems of thermoelasticity for anisotropic bodies with cuts. II.
Behavior of critical solutions of a nonlocal hyperbolic problem in Ohmic heating of foods.
Behaviour Near the Boundary of Positive Solutions of Second-Order Parabolic Equations.
Behaviour near zero and near infinity of solutions to elliptic equalities and inequalities.
Behaviour of global solutions for a system of reaction-diffusion equations from combustion theory
We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.
Behaviour of solutions to as p → +∞
Behaviour of symmetric solutions of a nonlinear elliptic field equation in the semi-classical limit: Concentration around a circle.
Behaviour of the first eigenvalue of the p-Laplacian in a domain with a hole
We investigate the behaviour of a sequence , s = 1,2,..., of eigenvalues of the Dirichlet problem for the p-Laplacian in the domains , s = 1,2,..., obtained by removing from a given domain Ω a set whose diameter vanishes when s → ∞. We estimate the deviation of from the eigenvalue of the limit problem. For the derivation of our results we construct an appropriate asymptotic expansion for the sequence of solutions of the original eigenvalue problem.
Behaviour of the support of the solution appearing in some nonlinear diffusion equation with absorption
Numerical experiments suggest interesting properties in the several fields of fluid dynamics, plasma physics and population dynamics. Among such properties, we may observe the interesting phenomena; that is, the repeated appearance and disappearance phenomena of the region penetrated by the fluid in the flow through a porous media with absorption. The model equation in two dimensional space is written in the form of the initial-boundary value problem for a nonlinear diffusion equation with the effect...
Benjamin-Ono equation on a half-line.
Benjamin–Ono periodic bifurcating water waves in presence of an essential spectrum
Bergman Spaces For The Solutions Of Linear Partial Differential Equations.
Bernstein and De Giorgi type problems: new results via a geometric approach
We use a Poincaré type formula and level set analysis to detect one-dimensional symmetry of stable solutions of possibly degenerate or singular elliptic equations of the formOur setting is very general and, as particular cases, we obtain new proofs of a conjecture of De Giorgi for phase transitions in and and of the Bernstein problem on the flatness of minimal area graphs in . A one-dimensional symmetry result in the half-space is also obtained as a byproduct of our analysis. Our approach...
Besov Regularity for Second Order Elliptic Boundary Value Problems with Variable Coefficients.
Best possible estimates of solutions to the transmission problem for the Laplace operator with N different media in a conical domain
We investigate the behavior of weak solutions to the transmission problem for the Laplace operator with N different media in a neighborhood of a boundary conical point. We establish a precise exponent of the decreasing rate of the solution.