On the semilinear heat equations with time-lag

Feedback Stabilization of Semilinear Heat Equations

Holomorphic Solutions of Semilinear Heat Equations

with φ ∈ L(R), where P is a polynomial vanishing at the origin and ∆ stands for the Laplacian with respect to x. The analyticity in time of the solutions of a semilinear heat equation has been considered by many authors. For example Ōuchi [2] treated the analyticity in time of the solutions of certain initial boundary value problems with bounded continuous initial functions, which include (1) i...

Singular perturbations to semilinear stochastic heat equations

We consider a class of singular perturbations to the stochastic heat equation or semilinear variations thereof. The interesting feature of these perturbations is that, as the small parameter ε tends to zero, their solutions converge to the ‘wrong’ limit, i.e. they do not converge to the solution obtained by simply setting ε = 0. A similar effect is also observed for some (formally) small stocha...

On Blow-up at Space Infinity for Semilinear Heat Equations

We are interested in solutions of semilinear heat equations which blow up at space infinity. In [7], we considered a nonnegative blowing up solution of ut = ∆u+ u, x ∈ R, t > 0 with initial data u0 satisfying 0 ≤ u0(x) ≤ M, u0 ≡ M and lim |x|→∞0 = M, where p > 1 and M > 0 is a constant. We proved in [7] that the solution u blows up exactly at the blow-up time for the spatially constant solution...

On semilinear elliptic equations with global coupling

We consider the problem