Pavol Quittner Philippe Souplet Blow-up, Global Existence and Steady States Second
Edition Page 1 Birkhäuser Advanced Texts Basler Lehrbücher Pavol Quittner Philippe …

The Cauchy problem for the semilinear heat equations is studied in the Orlicz space expL2
(Rn), where any power behavior of interaction works as a subcritical nonlinearity. We prove …

We study singular radial solutions of the semilinear elliptic equation Δ u+ f (u)= 0 Δ u+ f (u)=
0 on finite balls in R^ N RN with N ≥ 3 N≥ 3. We assume that f satisfies either f (u)= u^ p+ o …

We study the simplest parabolic-elliptic model of chemotaxis in space dimensions N≥ 3,
and show the optimal conditions on the initial data for the finite time blow-up and the global …

A positive radial singular solution for Δ u+ f (u)= 0 with a general supercritical growth is
constructed. An exact asymptotic expansion as well as its uniqueness in the space of radial …

By introducing a new classification of the growth rate of exponential functions, singular
solutions for semilinear elliptic equations in 2-dimensions with exponential nonlinearities …

The Cauchy problem in R n is considered for the Keller–Segel system ut= Δ u-∇·(u∇ v), 0=
Δ v+ u,(⋆) with a focus on a detailed description of behavior in the presence of nonnegative …

We provide a complete classification with respect to asymptotic behaviour, stability and
intersections properties of radial smooth solutions to the equation− Δ gu= eu on Riemannian …

In the present article, we are concerned with the following problem: vt= Δ v+∣ x∣ β ev, x∈
RN, t> 0, v (x, 0)= v 0 (x), x∈ RN, where N≥ 3, 0< β< 2, and v 0 is a continuous function in …

We are concerned with the existence of global in time solution for a semilinear heat equation
with exponential nonlinearity (P){∂ tu= Δ u+ eu, x∈ RN, t> 0, u (x, 0)= u 0 (x), x∈ RN, where …