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In this paper, we prove the common fixed point theorems for weakly compatible mappings in non-Archimedean Menger PM-spaces, that use the common limit range property. In addition, we give some examples of these results. Then we will extend our main result to four finite families of self-mappings by the notion of pairwise commuting. Finally, we will give applications for our main theorem. [ABSTRACT FROM AUTHOR]

In this paper, we evaluate certain type superlinear nonlocal problems that are a class of parabolic equations with the second-type integral condition. We use the Fadeo-Galarkin method to establish the existence of the weak solution and we prove the uniqueness of this solution for the problem by using an a priori estimate. In addition, we study the theoretical blow-up solution and perform several numerical simulations of finite-time blow-up of a particular example of the main problem. [ABSTRACT FROM AUTHOR]