Papers by Sujeewa Hapuarachchi
Mathematical methods in the applied sciences, Jun 29, 2016
REGULARIZED SOLUTIONS FOR TERMINAL PROBLEMS OF PARABOLIC EQUATIONS Sujeewa Indika Hapuarachchi Ju... more REGULARIZED SOLUTIONS FOR TERMINAL PROBLEMS OF PARABOLIC EQUATIONS Sujeewa Indika Hapuarachchi July 20, 2017 The heat equation with a terminal condition problem is not well-posed in the sense of Hadamard so regularization is needed. In general, partial differential equations (PDE) with terminal conditions are those in which the solution depends uniquely but not continuously on the given condition. In this dissertation, we explore how to find an approximation problem for a nonlinear heat equation which is well-posed. By using a small parameter, we construct an approximation problem and use a modified quasi-boundary value method to regularize a time dependent thermal conductivity heat equation and a quasi-boundary value method to regularize a space dependent thermal conductivity heat equation. Finally we prove, in both cases, the approximation solution converges to the original solution whenever the parameter goes to zero.
REGULARIZED SOLUTIONS FOR TERMINAL PROBLEMS OF PARABOLIC EQUATIONS Sujeewa Indika Hapuarachchi Ju... more REGULARIZED SOLUTIONS FOR TERMINAL PROBLEMS OF PARABOLIC EQUATIONS Sujeewa Indika Hapuarachchi July 20, 2017 The heat equation with a terminal condition problem is not well-posed in the sense of Hadamard so regularization is needed. In general, partial differential equations (PDE) with terminal conditions are those in which the solution depends uniquely but not continuously on the given condition. In this dissertation, we explore how to find an approximation problem for a nonlinear heat equation which is well-posed. By using a small parameter, we construct an approximation problem and use a modified quasi-boundary value method to regularize a time dependent thermal conductivity heat equation and a quasi-boundary value method to regularize a space dependent thermal conductivity heat equation. Finally we prove, in both cases, the approximation solution converges to the original solution whenever the parameter goes to zero.
Mathematical Methods in the Applied Sciences
Mathematical Methods in the Applied Sciences, 2016
Backward heat equation with time dependent variable coefficient is severely ill-posed in the sens... more Backward heat equation with time dependent variable coefficient is severely ill-posed in the sense of Hadamard, so we need regularization. In this paper, we consider Backward heat equation with time dependent variable coefficient, and by small perturbing, we obtain an approximation problem. We show this approximation problem is well-posed with small parameter. Also, we show this approximation system converges to the original problem when parameter goes to zero. Here, we use modified-quasi boundary value method to regularize this problem.
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Papers by Sujeewa Hapuarachchi