Reinhard Redlinger

A theorem of La Salle-Lyapunov type for parabolic systems

This paper deals with the boundary value problem for a nonlinear system of parabolic differential equations for

Compactness results for time-dependent parabolic systems

u = u(t,x)

Quenching in Time-Delay Systems: A Summary and a Counterexample

\[ u_t = Lu + f(u)\quad {\text{in }}\Omega ,\quad u(0,x){\text{ given}},\...

On the Asymptotic Behavior of a Semilinear Functional Differential Equation in Banach Space

(k = 1, 2 ,..., N), where u = (u’,..., 8) is a function of (t, X) E G, 24) = ad/at, Q c R” is a bounded domain with smooth boundary LX!, Ak are uniformly elliptic operators and Bk linear boundary operators. We say that u is a regular solution of (l), if the function u together with its derivatives appearing in (1) is continuous in G such that Eqs. (1) are identically satisfied. It is the object of this paper to show that under suitable conditions on A, B, and g the orbit T(u,) = {a(& .): t B O> of a bounded regular solution of (1) is relatively compact in C2(fl, W”). Results of this type are essential for the study of the asymptotic behavior of solutions u of (1); see, e.g., [6, Sect. 4.61 or [17, p. 3.551. We will deduce our theorems from more general results valid for abstract nonlinear evolution equations of the form

Multiplicity results for asymptotically homogeneous semilinear boundary value problems

This paper combines the salient features of two separate investigations. The first pertains to existence theorems for parabolic-functional systems and is based upon the Karlsruhe dissertation of the second author. The relevance of these results is that they permit a time delay and they do not require the functions to be Lipschitzian. Thus the equation for the unknown function

The spectral radius and Liapunov's theorem

u(t,x)

Existence theorems for semilinear parabolic systems with functionals

can contain such terms as

GASFLOW-MPI: A new 3-D parallel all-speed CFD code for turbulent dispersion and combustion simulations Part II: First analysis of the hydrogen explosion in Fukushima Daiichi Unit 1

u(t - \mu (t),x)

Invariant sets for strongly coupled reaction-diffusion systems under general boundary conditions

,

GASFLOW-MPI: A new 3-D parallel all-speed CFD code for turbulent dispersion and combustion simulations: Part I: Models, verification and validation

|u(t,x)|^\lambda