We are concerned here with well-posed problems for the partial differential equation uₜ(x, t) + yMuₜ(x, t) + Lu(x, t) = f(x, t) containing the elliptic differential operator M of order 2m and the differential operator L of order ≤2m. Hilbert space methods are used to formulate and solve an...
An existence theory is developed for a semilinear evolution equation in Banach space which is modeled on boundary value problems for partial differential equations of Sobolev type. The operators are assumed to be measurable and to satisfy coercive estimates which are not necessarily uniform in their time dependence, and to...
The L²-error estimates are established for the continuous time Faedo-Galerkin approximation to solutions of a linear parabolic initial boundary value problem that has elliptic part of order 2m. Properties of analytic semigroups are used to obtain these estimates directly from the L²-estimates for the corresponding steady state elliptic problem under...
The Cauchy problem for the evolution equation Mu’(t) + N(t,u(t)) = 0 is studied, where M and N(t,•) are, respectively, possibly degenerate and nonlinear monotone operators from a vector space to its dual. Sufficient conditions for existence and for uniqueness of solutions are obtained by reducing the problem to an...
We give a nonstandard method of integrating the equation Bu" + Cu’ + Au = f in Hilbert space by reducing it to a first order system in which the differentiated term corresponds to energy. Semigroup theory gives existence for hyperbolic and for parabolic cases. When C = εA, ε...
The initial-value problem is studied for evolution equations in Hilbert space of the general form d/dt A(u) + B(u) ϶ f, where and are maximal monotone operators. Existence of a solution is proved when A is a subgradient and either is strongly monotone or B is coercive; existence is established...
Diffusion in a fissured medium with absorption or partial saturation effects leads to a pseudoparabolic equation nonlinear in both the enthalpy and the permeability. The corresponding initial-boundary value problem is shown to have a solution in various Sobolev-Besov spaces, and sufficient conditions are given for the problem to be well-posed.
A system of quasilinear degenerate parabolic equations arising in the modeling of diffusion in a fissured medium is studied. There is one such equation in the local cell coordinates at each point of the medium, and these are coupled through a similar equation in the global coordinates. It is shown...
A general porous-medium equation is uniquely solved subject to a pair of boundary conditions for the trace of the solution and a second function on the boundary. The use of maximal monotone graphs for the three nonlinearities permits not only the inclusion of the usual boundary conditions of Dirichlet, Neumann,...
We develop the theory of degenerate and nonlinear evolution systems in mixed formulation.
It will be shown that many of the well-known results for the stationary problem extend to
the nonlinear case and that the dynamics of a degenerate Cauchy problem is governed by a nonlinear
semigroup. The results are...
We explore two characteristic features of x-ray computed tomography inversion formulas in two and
three dimensions that are dependent on π-lines. In such formulas the data from a given source
position contribute only to the reconstruction of ƒ(x) for x in a certain region, called the region
of backprojection. The...
Transcriptome analysis of Pseudomonas fluorescensSBW25 showed that 702 genes were differentially regulated in a gacS::Tn5 mutant, with 300 and 402 genes up- and downregulated respectively. Similar to the Gac regulon of other Pseudomonas species, genes involved in motility, biofilm formation, siderophore biosynthesis and oxidative stress were differentially regulated in the...
The Pseudomonas aeruginosa antimetabolite L-2-amino-4-methoxy-trans-3-butenoic acid (AMB) shares biological activities with 4-formylaminooxyvinylglycine, a related molecule produced by Pseudomonas fluorescens WH6. We found that culture filtrates of a P.aeruginosa strain overproducing AMB weakly interfered with seed germination of the grassy weed Poa annua and strongly inhibited growth of Erwinia amylovora, the...
Agriculture is now facing the ‘perfect storm’ of climate change, increasing costs of fertilizer and rising food demands from a larger and wealthier human population. These factors point to a global food deficit unless the efficiency and resilience of crop production is increased. The intensification of agriculture has focused on...