in this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete riemannian manifold floating in space rn+1and is tangent to the space rn at ∂h0(t); (2...

In this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the Cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. Our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete Riemannian manifold floating in space RN+1and is tangent to the space RN at ∂H0(t); (2...

in this paper, sufficient conditions are investigated for the existence of periodic (not necessarily positive) solutions for nonlinear several time delay population system with feedback control. nonlinear system affected by an periodic external source is studied. existence of a control variable provides  the extension of  some previous results obtained in other studies. we give a illustrative e...

In this paper, sufficient conditions are investigated for the existence of periodic (not necessarily positive) solutions for nonlinear several time delay population system with feedback control. Nonlinear system affected by an periodic external source is studied. Existence of a control variable provides  the extension of  some previous results obtained in other studies. We give a illustrative e...

Blind audio source separation (BASS) arises in a number of applications in speech and music processing such as speech enhancement, speaker diarization, automated music transcription etc. Generally, BASS methods consider multichannel signal capture. The single microphone case is the most difficult underdetermined case, but it often arises in practice. In the approach considered here, the main so...

We study controllability of 2D defocusing cubic Schroedinger equation under periodic boundary conditions and control applied via source term (additively). The source term is a linear combination of few complex exponentials (modes) with time-variant coefficients controls. We manage to prove that controlling just 4 modes one can achieve controllability of this equation in any finite-dimensional p...

We show that the Perron-Frobenius equation of microscopic chaos based on double symmetric maps leads to an inhomogeneous Smoluchowski equation with a source term. Our perturbative analysis reveals that the source term gives rise to a directed current for a strongly damped particle in a spatially periodic potential. In addition, our result proves that in the zeroth-order limit, the position dist...

A parabolic PDE with hysteresis in the source term is considered. The existence of periodic solutions for a general hysteresis operator is proven and an asymptotic result for solutions of this equation, using ideas due to Krejč́ı, is obtained.