Periodic solutions of a quasilinear parabolic differential equation

Periodic solutions of fourth-order delay differential equation

In this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(t-tau(t)))+g(dot{x}(t-tau(t)))+h({x}(t-tau(t)))=p(t)$  is investigated. Some new positive periodic criteria are given.  

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Computing Optimal Control with a Quasilinear Parabolic Partial Differential Equation

This paper presents the numerical solution of a constrained optimal control problem (COCP) for quasilinear parabolic equations. The COCP is converted to unconstrained optimization problem (UOCP) by applying the exterior penalty function method. Necessary optimality conditions for the considered problem are established. The computing optimal controls are helped to identify the unknown coefficien...

Time-periodic Solutions of Quasilinear Parabolic Differential Equations Ii. Oblique Derivative Boundary Conditions

We study boundary value problems for quasilinear parabolic equations when the initial condition is replaced by periodicity in the time variable. Our approach is to relate the theory of such problems to the classical theory for initial-boundary value problems. In the process, we generalize many previously known results.

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 ...