On strong solutions of a Robin problem modelling heat conduction in materials with corroded boundary

Blow-up and non-extinction for a nonlocal parabolic equation with logarithmic nonlinearity

“…Because of this main difficulty, some most effective methods, such as the method of upper and lower solutions, are not valid here anymore. Inspired by the ideas in [9][10][11][12][13][14][15][16][17][18], the threshold results for the global existence and blow-up of the weak solutions are given by the potential well method, the classical Galerkin method, and the logarithmic Sobolev inequality. Further we discuss the non-extinction properties and the asymptotic behavior of the global solutions.…”

Completness of roots elementes of linear operators in Banach spaces and application

“…We prove that, the spectrum of the associated differential operator is discrete and the system of roots elements are complete in E-valued weighted L p spaces. Note that, differential-operator equations (DOEs) have been studied extensively by many researchers (see [1,3] , [7,9,11,13,14] , [16][17][18][19][20][21][22][23][24][25][26] and the references therein).…”

Differential operators in exterior domain and application

“…Boundary value problems (BVPs) for differential-operator equations (DOEs) have been studied extensively by many researchers (see [3,5,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]26] and the references therein). A comprehensive introduction to the DOEs and historical references may be found in [13] and [26] .…”

“…A comprehensive introduction to the DOEs and historical references may be found in [13] and [26] . The maximal regularity properties for differential operator equations have been studied in [2] , [8] , [9] and [17][18][19][20][21][22][23] for instance. The main objective of the present paper is to discuss the exterior BVPs for the following DOE with variable coefficients εau (2) (x) + Au (x) + ε…”