Sentence examples for maximum principles the from inspiring English sources
By constructing some auxiliary functions and using maximum principles, the sufficient conditions were obtained there for the existence of global and blow-up solutions.
We present a robust computational framework for advective diffusive reactive systems that satisfies maximum principles, the non-negative constraint, and element-wise species balance property.
By constructing auxiliary functions and using maximum principles, the sufficient conditions characterized by functions f, g and u 0 were given for the existence of a blow-up solution.
Under appropriate assumptions on the functions a, b, f, g and h, by constructing auxiliary functions and using maximum principles, the sufficient conditions for the existence of global solution or blow-up solution, an upper estimate of the global solution, an upper bound of the blow-up time and an upper estimate of the blow-up rate were specified.
By constructing auxiliary functions and using maximum principles, the sufficient conditions for the existence of the blow-up solution, the sufficient conditions for the global existence of the solution, an upper bound for the 'blow-up time', and some explicit exponential decay bounds for the solution and its derivatives are specified.
Although the difference scheme does not satisfy the discrete maximum principle, the maximum norm stability of the scheme is established.
By employing Pontryagin's maximum principle, the optimal solution is acquired when the emergency response incurs nonlinear costs.
By constructing an appropriate Hamiltonian function and using Pontryagin's maximum principle, the optimal harvesting policy has been discussed.
By use of the Pontryagin's maximum principle the optimality condition in form of a depressed quartic equation is obtained.
To enforce the discrete maximum principle, the standard Galerkin discretization is constrained using a local extremum diminishing flux limiter.
According to the Maximum Principle, the maximum of u x,t) must be on the parabolic boundary, from which we obtain that (4.7) .
