东北电力大学偏微分方程前沿问题学术研讨会系列学术报告已于7月24日如期进行。会议邀请吉林大学高文杰教授致开幕词，与会专家进行全体合影留念。随后，分别由吉林大学郭斌教授、贵州财经大学李仲庆副教授、河海大学廖梦兰副教授和长春理工大学李晓蕾博士带来了四场仅精彩的学术报告。详细信息如下。
地点：吉林市利雅德饭店（二楼翠竹厅）
时间：7月24日上午8:00-11:00、下午14:00-17:00
会议报告相关信息如下：
Asymptotic behavior of an integral inequality and its application
吉林大学 郭斌
Abstract：In this talk, we first establish the lemma regarding the asymptotic behaviour of an integral inequality by using comparison principle, Furthermore, with the help of this lemma, we study the convergence rate of three classes of nonlinear evolution equations. In addition, we propose some further problems.
Existence Results for Nonlinear Parabolic Equations with Nonstandard Growth and Gradient Terms in Lorentz Spaces
贵州财经大学 李仲庆
Abstract：In this report, we focus on an existence result for a class of nonlinear parabolic equations that include a gradient term and data in L1. The main challenges arise from the p(⋅,⋅)-structure and the lower-order term with coefficients in Lorentz spaces. To handle the gradient term without imposing a sign condition, we partition the entire time interval into several subintervals. On each subinterval, within the framework of functional spaces with variable exponents, we derive Marcinkiewicz and Lorentz estimates to obtain bounds for the truncation energy. Using these a priori estimates, we demonstrate the almost everywhere convergence of the gradient sequence, which is essential for passing to the limit and establishing the existence of solutions.
Fourth-order wave equations with variable-exponent nonlinearity and mixed dampings
河海大学 廖梦兰
Abstract：In this talk, we consider the Petrovsky equation with damping and nonlinear source under initial-boundary value conditions. The upper bound of the blow-up time is derived for low initial energy using the differential inequality technique. For m(x) is equal to 2, in particular, the upper bound of the blow-up time is obtained by the combination of Levine's concavity method and some differential inequalities under high initial energy. For the essential infimum of m(x) is larger than 2, the blow-up phenomenon will happen for arbitrarily high initial energy. In addition, by making full use of the strong damping, the lower bound of the blow-up time is discussed. Moreover, the global existence of solutions and an energy decay estimate are presented by establishing some energy estimates.
Blow-up and decay for the Mindlin-Timoshenko plate model with supercritical exponents
长春理工大学 李晓蕾
Abstract：The Mindlin-Timoshenko(MT) plate model designed to analyze the static and dynamic behavior of moderately thick plates and shells, addressing limitations inherent in classical Kirchhoff plate theory by incorporating transverse shear deformation and rotary inertia effects. We all know that for the supercritical cases, the failure of the Sobolev embedding inequality makes the classical method be impossible. In this talk, we will discuss the methods to analyse the finite-time blow-up of the solution with the supercritical source and logarithmic energy decay rates with the supercritical damping.
来源：孙再臣
初审：刘鲍
复审：袁丽峰
终审：李鹏松
