Peter Weidemaier

Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed _{}-norm

We determine the exact regularity of the trace of a function u ∈ Lq (0, T ; W 2 p (Ω)) ∩W 1 q (0, T ; Lp (Ω)) and of the trace of its spatial gradient on ∂Ω × ( 0, T ) in the regime p ≤ q. While for p = q both the spatial and temporal regularity of the traces can be completely characterized by fractional order Sobolev-Slobodetskii spaces, for p 6= q the Lizorkin-Triebel spaces turn out to be necessary for characterizing the sharp temporal regularity.

Local existence for parabolic problems with fully nonlinear boundary condition; anLp-approach

SummaryWe study the problem (ai=ai (x, t, u, p)) (which is of variational form and arises in heat conduction) in the Sobolev Space Wp2 (Ω × × (0, T)), Ω (Rn, p>n+2. Existence of a local (in time) solution is proved under a natural compatibility condition between the data (Theorem 2.1). This solution is also globally unique. An outlook to similar problems for parabolic systems is given (section 4). Our method also applies to quasilinear equations with conormal b.c. (cf. (P), end of section 2).

Refinement of an L p -estimate of Solonnikov for a parabolic equation of the second order with conormal boundary condition

On affine une estimation L p de Solonnikov pour le probleme aux valeurs limites et initiales suivant: w t― Δw=f dans R + n X(0,T); −∂ n w| xd n d = d 0=Ψ dans R n−1 X(0,T), w(0)=w 0 dans R + n

A Combined Experimental/Computational Approach for Assessing the High Strain Rate Response of High Explosive Simulants and Other Viscoelastic Particulate Composite Materials

The quasistatic and dynamic mechanical properties of a viscoelastic particulate composite employed as a surrogate, cast‐cure high explosive were determined from uniaxial compression experiments at strain rates up to 107 sec−1. The results from these experiments were used to obtain parameters for a non‐linear viscoelastic material model. The viscoelasticity described by the macroscopic material model introduced in this paper affects not only the deviatoric components of stress and strain but the volumetric components as well. The material description is adequate for reproducing experimentally observed responses at loading rates ranging from quasistatic to shock levels with a single set of material parameters. Parameters for an HTPB‐sugar composite are provided.

On L p -Estimates of Optimal Type for the Parabolic Oblique Derivative Problem with VMO-Coefficients — A Refined Version

We prove Wp2,1 (ΩT)-estimates (1 < p < ∞) for parabolic operators with a second-order elliptic part in non-divergence form with essentially bounded VMO-coefficients. The boundary condition Σin=1 b i (ξ, t)∂iu(ξ, t) = g(ξ, t) on ∂ΩT is considered in the non-degenerate case, and the b i are only assumed to be in space-time Sobolev-spaces (see condition (B)).