We study the variational formulation of the obstacle problem in unbounded domains when the force term might grow at infinity. We derive the appropriate variational formulation and prove existence and uniqueness of solution. We also show the rate of growth at infinity of the solution in terms of the growth rates of the obstacle and the force, and prove the exponential convergence of the solutions in approximating bounded domains to the solution in the unbounded domain.
Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.
Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.
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