Lambertus A. Peletier

Uniqueness of positive solutions of semilinear equations in ℝn

A floating seat cushion which is capable of emergency use as a life preserver. The seat cushion comprises a center core of open cell polyurethane foam material surrounded by an outer layer of closed cell polyethylene foam material. A belt extends transversely adjacent one side of the center core to form a pair of loops which extend outwardly from opposite sides of the cushion. The belt is preferably laminated between the center core and outer layer. The cushion is preferably formed by placing the center core outer layer and belt in overlying relationship to each other with adhesive between them. The assembly is then placed in a press and compressed to cause the center core to collapse so that the peripheral portions of the outer layer can be bonded together to enclose the center core. Air is then replaced into the center core to cause the cushion to assume a convex or crown shape. The completed cushion is preferably coated with vinyl.

A New Class of Entropy Solutions of the Buckley–Leverett Equation

We discuss an extension of the Buckley–Leverett (BL) equation describing two-phase flow in porous media. This extension includes a third order mixed derivatives term and models the dynamic effects in the pressure difference between the two phases. We derive existence conditions for traveling wave solutions of the extended model. This leads to admissible shocks for the original BL equation, which violate the Oleinik entropy condition and are therefore called nonclassical. In this way we obtain nonmonotone weak solutions of the initial-boundary value problem for the BL equation consisting of constant states separated by shocks, confirming results obtained experimentally.

Elliptic equations with nearly critical growth

> (N f 2)/(N - 2) it has no solution for any (star-shaped) domain [13]. Recently, considerable interest has grown around problems like (I) in which the right hand side up is replaced by a perturbation f(u) of the pure power, such as f(u) = Au” + up, where 1 E Iw and 0 <

Spatial patterns described by the extended Fisher-Kolmogorov equation: periodic solutions

Stationary antisymmetric single-bump periodic solutions of a fourth-order generalization of the Fisher--Kolmogorov (FK) equation are analyzed. The coefficient

Positivity versus localization in degenerate diffusion equations

\gamma > 0

Emden-Fowler equations involving critical exponents

of the additional fourth-order spatial derivative is found to be a critical parameter. If

EXACT HOMOCLINIC AND HETEROCLINIC SOLUTIONS OF THE GRAY-SCOTT MODEL FOR AUTOCATALYSIS*

\gamma \leq {1 \over 8}

Allometric scaling of pharmacodynamic responses: application to 5-Ht1A receptor mediated responses from rat to man.

, the family of periodic solutions is still very similar to that of the FK equation. However, if

A very singular solution of the porous media equation with absorption

\gamma > {1 \over 8}

Dynamics of target-mediated drug disposition: characteristic profiles and parameter identification

, it is possible to distinguish different families of periodic solutions and the structure of such solutions is much richer.