Soheil Salahshour 1, Ali Ahmadian 2, Fudziah Ismail 2 and Dumitru Baleanu 3,4,* 1 Young Researchers and Elite Club, Islamic Azad University, Mobarakeh Branch, Mobarakeh, Iran; [email protected] 2 Department of Mathematics, Faculty of Science, Universti Putra Malaysia, 43400 Selangor, Malaysia; [email protected] (A.A.); [email protected] (F.I.) 3 Department of Mathematics and...

parameterized by μ > 0, and prove a representation theorem for its solutions using the theory of special functions. This representation is used to obtain Lp–Lq estimates for the solution and for the energy operator corresponding to this Cauchy problem. Especially for the L2 energy estimate we determine the part of the phase space which is responsible for the decay rate. It will be shown that th...

This work is devoted to proving existence of global weak solutions for a general isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985) [5], which can be used as a phase transition model. We distinguish two cases when the dimension N = 2 and N = 1, in the first case we need that 1 ρ ∈ L∞, when N = 1 we get a weak solution in finite time in the energy space.

We prove an existence result for a coupled system of the reactiondiffusion kind. The fact that no growth condition is assumed on some nonlinear terms motivates the search of a weak-renormalized solution.