INITIAL-BOUNDARY VALUE PROBLEM FOR HIGHER-ORDERS NONLINEAR PARABOLIC EQUATIONS WITH VARIABLE EXPONENTS OF THE NONLINEARITY IN UNBOUNDED DOMAINS WITHOUT CONDITIONS AT INFINITY

Attractors for Parabolic Equations with Nonlinear Boundary Conditions, Critical Exponents, and Singular Initial Data

Initial - Boundary Value Problems for Parabolic Equations

On stability with respect to boundary conditions for anisotropic parabolic equations with variable exponents

*Correspondence: [email protected] School of Applied Mathematics, Xiamen University of Technology, Xiamen, China Abstract The anisotropic parabolic equations with variable exponents are considered. If some of diffusion coefficients {bi(x)} are degenerate on the boundary, the others are always positive, then how to impose a suitable boundary value condition is researched. The existence of weak...

Initial-Boundary Value Problem for Hyperbolic Equations

where Ji = 0 for x0 < 0. The problem is to find necessary and sufficient conditions on B(x, B) such that the initial-boundary value problem (1), (2), (3) is well-posed. Note that all theorems that a;re formulated below will also apply to the case when (1) is a general hyperbolic equation or a hyperbolic system of equations of arbitrary order provided that all components of the characteristic co...

Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations

This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ...