Abstract
We prove existence-uniqueness theorems for some kinds of nonlinear parabolic equations (cf. [2, 3, 15]) with singular initial data and non- Lipschitz’s nonlinearities in a framework of Colombeau’s algebras using different kinds of regularization for singularities appearing in the equations. We establish the convergence of a family of regularized solutions to the classical solutions (if they exist), when nonlinear term g(u) is of Lipschitz’s class and ε → 0. Moreover, we find solutions not available in classical approach.
Citation
Mirjana Stojanović. "REGULARIZATION FOR HEAT KERNEL IN NONLINEAR PARABOLIC EQUATIONS." Taiwanese J. Math. 12 (1) 63 - 87, 2008. https://doi.org/10.11650/twjm/1500602489
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