Messaoudi and Said-Houari [17] dealt with the problem (1.7) and proved a global nonexistence of solutions for a large class of initial data for which the initial energy takes positive values.
Considering a relaxed version of these optimal design problems, we show and characterize the emergence of different phenomena for the first problem depending on the choice of the initial data: existence of optimal sets having a finite or an infinite number of connected components, or nonexistence of an optimal set (relaxation phenomenon).
Furthermore, we shall prove that for any positive initial energy there are initial data implying nonexistence of global solutions.
Nonetheless, the lack of segregation data, the nonexistence of functional data for this variant and the in silico prediction by PolyPhen of non-pathogenicity, support a benign outcome for this genetic change in AD pathogenicity.
Finally, we shall prove that if the initial data satisfy (8), there exists (mathcal{I}_{Q u_{0},v_{0})}) such that it contains the interval ((eta_{frac{r - 2}{2} u_{{0},v_{0}),mu_{lambda} u_{0},v_{0}) )) for some (0 < lambda< 1), and hence any initial energy here produces nonexistence of global solutions.
In case of nonexistence of observed infiltration data, this novel model can be used to artificially generate infiltration data for NIT campus.
For example, in [9, 10], Bǎleanu et al. investigated the existence and nonexistence of the solutions for initial value problem of the following linear sequential fractional differential equation: bigl(D_{0}^{alpha}ybigr)'+a(x y=0, quad x>0.
First, the test of the data being random was conducted using the Mann Kendall method (recommended by the global meteorology department) to determine the existence or nonexistence of any sort of the data trend.
Then, as (Q u_{0},v_{0})) is the larger set of initial energies that produces nonexistence of global solutions, the largest initial energy with this property is closer to (frac{1}{2}Phi(u_{0},v_{0})).
Our interest is the blow-up of spatial derivatives of solutions in finite time to the initial boundary value problem (1.2) and the nonexistence of the weak solutions to the initial value problem (1.3).
In 1999, Vitillaro [10] proved the global nonexistence of the solutions with positive initial energy.
