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Friday, December 17, 2004

**Abstract:** Some fundamental laws of physics are stated as "conservation of X". In one space dimension, a general conservation law can be formulated mathematically as the vector partial differential equation u_t + f(u)_x = 0. In this talk, I will present an overview of the existence and qualitative theory of conservation laws, particularly focusing on my work about stability of large waves. Then I will touch upon recent work establishing a different kind of stability result for combustion waves in reaction-diffusion equations - these equations are not of conservation form.