On singular initial-boundary value problems for second order parabolic equations

Initial value problems for second order hybrid fuzzy differential equations

Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia

Initial - Boundary Value Problems for Parabolic Equations

Second order abstract initial - boundary value problems

Introduction Partial differential equations on bounded domains of R n have traditionally been equipped with homogeneous boundary conditions (usually Dirichlet, Neumann, or Robin). However, other kinds of boundary conditions can also be considered, and for a number of concrete application it seems that dynamic (i.e., time-dependent) boundary conditions are the right ones. Motivated by physical p...

Boundary Value Problems for Higher Order Parabolic Equations

We consider a constant coefficient parabolic equation of order 2m and establish the existence of solutions to the initial-Dirichlet problem in cylindrical domains. The lateral data is taken from spaces of Whitney arrays which essentially require that the normal derivatives up to order m−1 lie in L2 with respect to surface measure. In addition, a regularity result for the solution is obtained if...

Positive Solutions for Second-Order Singular Semipositone Boundary Value Problems

which arises in many different areas of applied mathematics and physics. Singular problems of this type that the nonlinearity g may change sign are referred to as singular semipositone problems in the literature. Motivated by BVP (1.1), this paper presents the existence results of the following second-order singular semipositone boundary value problem: { u ′′ + f(t, u) + g(t, u) = 0, 0 < t < 1,...