Modeling with diffirential equations and numerical methods for solving inverse problems

我们的目标是数学问题的对象，如数学模型，反问题的分析，和发展的数值技术共同的生物降解问题，其中高分子化合物降解的微生物和水蒸气两相流的水锤产生的行动。在管道如供水钢管中的液体流动中产生的压力波动，以及由对水锤反应的压降产生的压力波动。对于高分子化合物的生物降解，我们的目标是建立数学分析技术，如数学模型的建议，分析与介绍实验结果，并通过数值模拟验证模型的适当性。微生物解聚过程分为外源型和内源型，外源型降解仅限于分子末端，单体单元逐步分离，内源型降解分子在任意位置分离。我们进行了 ...更多信息 基于外源性解聚过程和内源性解聚过程模型的分析，其中降解速率仅取决于分子量。另一方面，在诸如微生物种群和温度的临时因素影响生物降解的情况下，有必要将这些临时因素引入降解速率中。假设降解速率是时间的函数和分子量的函数的产物，我们表明，一个模型被转化为一个变量的变化，其中的降解是独立于时间，和依赖于分子量的因素，可以得到与以前开发的技术分析。还获得了有关时间因素的结果。我们将实验结果引入分析，数值求解反问题，并模拟相对于分子量t的重量分布的过渡，以验证这种模型是适当的一般模型。少

We aimed at objects of mathematical problems such as mathematical models, analysis of inverse problems, and development of numerical techniques common to problems concerning biodegradation in which high molecular compounds are degraded by actions of microorganisms and water-vapor two-phase flow generated by waterhammer. pressure surge generated in liquid flow in pipelines such as steel pipes of water supply, and by pressure drop in reaction to waterhammer. For biodegradation of high molecular compounds, we aimed at establishment of mathematical techniques of analysis such as proposals of mathematical models, analysis with introduction of experimental results, and verification of propriety of model by numerical simulation. Microbial depolymerization processes are classified into exogenous type in which degradation is restricted to terminals of molecules and monomer units are separated stepwise, and endogenous type in which molecules are, separated at arbitrary positions. We conducted an … More alyses based on models for exogenous depolymerization processes and endogenous depolymerization processes, in which degradation rates depend only on molecular weight. On the other hand, in case temporary factors such as microbial population and temperature affect biodegradation, it becomes necessary to introduce those temporal factors into a degradation rate. Under the assumption that a degradation rate is a product of a function of time and a function of molecular weight, we showed that a model was transformed by a change of variable to one in which the degradation is independent of time, and that the factor dependent of molecular weight can be obtained with previously developed techniques of analysis. Results concerning temporal factor were also obtained. We introduced experimental results into analysis, solved inverse problems numerically, and simulated transitions of weight distribution with respect to molecular weigh t in order to verify that such models are appropriate as general models. Less