A Note on Maximal Rate of Decay for Solutions to Some Linear Wave Equations.
A note on measure-valued solutions to the full Euler system
We construct two particular solutions of the full Euler system which emanate from the same initial data. Our aim is to show that the convex combination of these two solutions form a measure-valued solution which may not be approximated by a sequence of weak solutions. As a result, the weak* closure of the set of all weak solutions, considered as parametrized measures, is not equal to the space of all measure-valued solutions. This is in stark contrast with the incompressible Euler equations.
A note on nodal non-radially symmetric solutions to Emden-Fowler equations.
A note on nonexistence of radial solutions to semilinear elliptic inequations.
We study the nonexistence result of radial solutions to -Δu + c u/(|x|2) + |x|σ|u|qu ≤ 0 posed in B or in B {0} where B is the unit ball centered at the origin in RN, N ≥ 3. Moreover, we give a complete classification of radial solutions to the problem -Δu + c u/(|x|2) + |x|σ|u|qu = 0. In particular we prove that the latter has exactly one family of radial solutions.
A note on nonhomogeneous initial and boundary conditions in parabolic problems solved by the Rothe method
When solving parabolic problems by the so-called Rothe method (see K. Rektorys, Czech. Math. J. 21 (96), 1971, 318-330 and other authors), some difficulties of theoretical nature are encountered in the case of nonhomogeneous initial and boundary conditions. As a rule, these difficulties lead to rather unnatural additional conditions imposed on the corresponding bilinear form and the initial and boundary functions. In the present paper, it is shown how to remove such additional assumptions in the...
A note on nonlinear elliptic systems involving measures.
A note on non-negative singular infinity-harmonic functions in the half-space.
In this work we study non-negative singular infinity-harmonic functions in the half-space. We assume that solutions blow-up at the origin while vanishing at infinity and on a hyperplane. We show that blow-up rate is of the order |x|-1/3.
A note on nontrivial periodic solutions of dynamical systems with subquadratic potential.
We obtain non-constant periodic solutions for a class of second-order autonomous dynamic systems whose potential is subquadratic at infinity. We give a theorem on conjugate points for convex potentials.
A Note on one dimensional symmetry in Carnot groups
In this Note we extend Gibbons conjecture to Carnot groups using the sliding method and the maximum principle in unbounded domains.
A note on poroacoustic traveling waves under Darcy's law: Exact solutions
A mathematical analysis of poroacoustic traveling wave phenomena is presented. Assuming that the fluid phase satisfies the perfect gas law and that the drag offered by the porous matrix is described by Darcy's law, exact traveling wave solutions (TWS)s, as well as asymptotic/approximate expressions, are derived and examined. In particular, stability issues are addressed, shock and acceleration waves are shown to arise, and special/limiting cases are noted. Lastly, connections to other fields are...
A note on propagation of singularities of semiconcave functions of two variables
P. Albano and P. Cannarsa proved in 1999 that, under some applicable conditions, singularities of semiconcave functions in propagate along Lipschitz arcs. Further regularity properties of these arcs were proved by P. Cannarsa and Y. Yu in 2009. We prove that, for , these arcs are very regular: they can be found in the form (in a suitable Cartesian coordinate system) , , where , are convex and Lipschitz on . In other words: singularities propagate along arcs with finite turn.
A note on -partial difference equations and some applications to generating functions and -integrals
We study the condition on expanding an analytic several variables function in terms of products of the homogeneous generalized Al-Salam-Carlitz polynomials. As applications, we deduce bilinear generating functions for the homogeneous generalized Al-Salam-Carlitz polynomials. We also gain multilinear generating functions for the homogeneous generalized Al-Salam-Carlitz polynomials. Moreover, we obtain generalizations of Andrews-Askey integrals and Ramanujan -beta integrals. At last, we derive ...
A note on quasilinear elliptic eigenvalue problems.
A note on radial nonlinear Schrödinger systems with nonlinearity spatially modulated.
A Note on Regular Points for Solutions of Elliptic Systems.
A note on regular points for solutions of nonlinear elliptic systems
It is shown in this paper that gradient of vector valued function solution of a nonlinear elliptic system, cannot be too close to a straight line without being regular.
A note on regularity for nonlinear elliptic systems
The - regularity of the gradient of weak solutions to nonlinear elliptic systems is proved.
A note on resonant frequencies for a system of elastic wave equations.
A note on Schrödinger operators with polynomial potentials
A Note on Shock Profiles in Dissipative Hyperbolic and Parabolic Models