In this article, we study the existence of solutions a parabolic-elliptic system partial differential equations describing behaviour biological species “ u $$ ” and chemical stimulus v in bounded regular domain ? \Omega ? N {\mathbb{R}}^N . The equation for is parabolic with nonlinear second order term chemotaxis type flux limitation as ? ? div ( | ? p 2 ) , -\chi \operatorname{div}\lef...

In this paper, we derive a dispersion relation for sound waves in viscous and heat conducting fluids. particular (i.e. variation of speed with frequency) is shown to be second order magnitude, w.r.t. Knudsen numbers, as the Stokes [2] case, corresponding non-conductive fluid (Prandtl number P r = $\infty$). This formula completes classical attenuation called Stokes-Kirchhoff. We represent simpl...

In this article, we first obtain an embedding result for the Sobolev spaces with variable-order, and then consider following Schrödinger–Kirchhoff type equations a+b∫Ω×Ω|ξ(x)−ξ(y)|p|x−y|N+ps(x,y)dxdyp−1(−Δ)ps(·)ξ+λV(x)|ξ|p−2ξ=f(x,ξ),x∈Ω,ξ=0,x∈∂Ω, where Ω is a bounded Lipschitz domain in RN, 1<p<+∞, a,b>0 are constants, s(·):RN×RN→(0,1) continuous symmetric function N>s(x,y)p all (x,...

In this work we deal with elliptic equations driven by the variable exponent double phase operator a Kirchhoff term and right-hand side that is just locally defined in terms of very mild assumptions. Based on an abstract critical point result Kajikiya (2005) recent priori bounds for generalized problems authors (Ho Winkert, 0000) , prove existence sequence nontrivial solutions whose L∞-norms co...