Measure Control of a Semilinear Parabolic Equation with a Nonlocal Time Delay

Solving the inverse problem of determining an unknown control parameter in a semilinear parabolic equation

The inverse problem of identifying an unknown source control param- eter in a semilinear parabolic equation under an integral overdetermina- tion condition is considered. The series pattern solution of the proposed problem is obtained by using the weighted homotopy analysis method (WHAM). A description of the method for solving the problem and nding the unknown parameter is derived. Finally, tw...

Optimal control of a semilinear parabolic equation with singular arcs

This paper develops a theory of singular arc, and the corresponding second order necessary and sufficient conditions, for the optimal control of a semilinear parabolic equation with scalar control applied on the r.h.s. We obtain in particular an extension of Kelley’s condition, and the characterization of a quadratic growth property for a weak norm.

Blow-up of a nonlocal semilinear parabolic equation with positive initial energy

Blow-up for a Semilinear Parabolic Equation with Nonlinear Memory and Nonlocal Nonlinear Boundary

where Ω is a bounded domain in RN for N ≥ 1 with C2 boundary ∂Ω, p, q, l and k are positive parameters, the weight function f (x, y) is nonnegative, nontrivial, continuous and defined for x ∈ ∂Ω, y ∈ Ω, while the nonnegative nontrivial initial Received November 14, 2012, accepted January 28, 2013. Communicated by Eiji Yanagida. 2010 Mathematics Subject Classification: 35B35, 35K50, 35K55.

Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition

In this paper, we consider a semilinear parabolic equation ut = ∆u + u q ∫ t 0 u(x, s)ds, x ∈ Ω, t > 0 with nonlocal nonlinear boundary condition u|∂Ω×(0,+∞) = ∫ Ω φ(x, y)u (y, t)dy and nonnegative initial data, where p, q ≥ 0 and l > 0. The blow-up criteria and the blow-up rate are obtained.