Periodic solutions of a quasilinear parabolic equation with nonlinear convection terms

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Periodic Solutions of a Nonlinear Parabolic Equation, Ii

Based on a strict coercivity estimate 8] for a class of nonlinear elliptic operators A : u 7 ! ra(; jruj)ru, it is shown that (with suitable consistency conditions on the data) the problem: _ u + Au = f; aru ~ n = '; time periodicity has a unique solution depending continuously on f; ' and also on the nonlin-ear form of the diiusion coeecient a(). This is then used to obtain existence by a xpoi...

Periodic Solutions of a Nonlinear Parabolic Equation, II1

Based on a strict coercivity estimate [8] for a class of nonlinear elliptic operators A : u 7→ ∇·a(·, |∇u|)∇u, it is shown that (with suitable consistency conditions on the data) the problem: u̇+ Au = f, a∇u · ~n = φ, time periodicity has a unique solution depending continuously on f, φ and also on the nonlinear form of the diffusion coefficient a(··). This is then used to obtain existence by a ...

Time Periodic Solutions for A Pseudo-parabolic Type Equation with Weakly Nonlinear Periodic Sources

In this paper, we prove the existence of nontrivial nonnegative time periodic solutions for a pseudo-parabolic type equation with weakly nonlinear periodic sources. Moreover, we investigate the asymptotic behavior of solutions as the viscous coefficient k tends to zero.

M. Badii PERIODIC SOLUTIONS FOR A NONLINEAR PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITIONS

In this paper we prove the existence of weak periodic solutions for a nonlinear parabolic equations with the Robin periodic boundary condition. The aim will be achieved by reformulating the problem in abstract form and applying some results of the maximal monotone mapping theory joint with the Schauder fixed point theorem.