Existence Of Solutions For A Class Of Quasilinear Parabolic Equations With Measure Coefficients

The time evolution of processes, such as movement of the planets, is very accurately modeled by differential equations. Such accurate modeling requires the identification of a small number of measurable quantities, like the positions and velocities of the planets, whose behavior over the time span considered is almost independent of the neglected factors.There are other important process, such as dynamical processes in physics, chemistry and biology can be described by differential equations depending on measure coefficients or parameters.Therefore,the process which look abstract can be solved this way.In the research of the electron mobility, pressure and pulse effect of the TLC conductor,proliferation of electronic leads to metal effect. In the flash when the switch is turned on (off) ,the migration process can be described by using the following equation:(?)u/(?)t-(?)~2u/(?)x~2=((?)u/(?)t) (δ(x)-δ(1-x)) 0 0 .At this special condition,the Equation (2) can be simplified as the following ordinary differential equation:y"(x) = f(x)(y~m(x))' + g(x), (3)where f(x) and g(x) are Lebesgue integrable functions.For the two cases that m > 1 and 0 < m < l,we will prove the existence of solution for Equation(3) respectively.