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...
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.