Browsing by Supervisor "Van der Walt, Jan Harm"

Browsing by Supervisor "Van der Walt, Jan Harm"

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  • An ergodic theoretic approach to Szemerédi's theorem 
    Van Amstel, Sarel Jakobus van der Walt (University of Pretoria, 2018)
    In this dissertation, Szemer edi's Theorem is proven using ergodic theoretic techniques via the Furstenberg Multiple Recurrence Theorem. Brief historical remarks, along with a non-technical layout of the ideas behind the ...
  • Existence results for a class of semi-linear initial value problems 
    Manicom, Gray Thomas (University of Pretoria, 2017)
    The main result of this thesis is an existence result for parabolic semi-linear problems. This is done by reformulating the semi-linear problem as an abstract Cauchy problem ut(t) = Au(t) + f(t; u(t)), t > 0 u(0) = u0 ...
  • Nonlinear theories of generalised functions 
    Agbebaku, Dennis Ferdinand (University of Pretoria, 2015)
    In this thesis, the Order Completion Method for nonlinear partial differential equation, in the setting of convergence spaces, is interpreted in terms of the algebraic theory of gen- eralised functions. In particular, ...
  • Semi-order units in vector lattices 
    Chitanga, Painos (University of Pretoria, 2021)
    The space C(X) of real-valued continuous functions on a topological space X is a vector lattice and a locally convex topological vector space, but what is the interaction between these structures? In the case of a compact ...
  • Solution of conservation laws via convergence space completion 
    Agbebaku, Dennis Ferdinand (University of Pretoria, 2011)
    It is well known that a classical solution of the initial value problem for a scalar conservation law may fail to exist on the whole domain of definition of the problem. For this reason, suitable generalized solutions of ...