Exact multiplicity of positive solutions in semipositone problems with concave-convex type nonlinearities.
Exact multiplicity of positive solutions to a superlinear problem.
Exact Neumann boundary controllability for second order hyperbolic equations
Using HUM, we study the problem of exact controllability with Neumann boundary conditions for second order hyperbolic equations. We prove that these systems are exactly controllable for all initial states in and we derive estimates for the control time T.
Exact null internal controllability for the heat equation on unbounded convex domains
The liner parabolic equation ∂y ∂t − 1 2 Δy + F · ∇ y = 1 x1d4aa; 0 u with Neumann boundary condition on a convex open domain x1d4aa; ⊂ ℝd with smooth boundary is exactly null controllable on each finite interval if 𝒪0is an open subset of x1d4aa; which contains a suitable neighbourhood of the recession cone of x1d4aa; . Here,F : ℝd → ℝd is a bounded, C1-continuous function, and F = ∇g, where g is convex and coercive.
Exact propagators for soliton potentials.
Exact relations for composites: Towards a complete solution.
Exact Schauder estimates of solutions of a boundary value problem for parabolic second order equations and their application to a nonlinear problem
We establish exact Schauder estimates of solutions of the transmission problem for linear parabolic second order equations with explicit dependence on the smoothness of the coefficients. Next we apply the estimates to the solvability of the nonlinear transmission problem.
Exact solution of the time fractional variant Boussinesq-Burgers equations
In the present article, we consider a nonlinear time fractional system of variant Boussinesq-Burgers equations. Using Lie group analysis, we derive the infinitesimal groups of transformations containing some arbitrary constants. Next, we obtain the system of optimal algebras for the symmetry group of transformations. Afterward, we consider one of the optimal algebras and construct similarity variables, which reduces the given system of fractional partial differential equations (FPDEs) to fractional...
Exact solutions and localized structures for higher-dimensional Burgers systems.
Exact solutions and symmetry operators for the nonlocal Gross-Pitaevskii equation with quadratic potential.
Exact solutions for a new fifth-order integrable system.
Exact solutions for a third-order KdV equation with variable coefficients and forcing term.
Exact solutions for equations of Bose-Fermi mixtures in one-dimensional optical lattice.
Exact solutions for nonclassical Stefan problems.
Exact solutions for the generalized BBM equation with variable coefficients.
Exact solutions of Cauchy problem for partial differential equations with double characteristics and singular coefficients
Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations
MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05In this paper a method for obtaining exact solutions of the multidimensional heat equations with nonlocal boundary value conditions in a finite space domain with time-nonlocal initial condition is developed. One half of the space conditions are local, and the other are nonlocal. Extensions of Duhamel principle are obtained. In the case when the initial value condition is a local one i.e. of the form u(x1; :::; xn; 0) = f(x1; :::; xn) the problem reduces...
Exact Solutions of Nonlocal Pluriparabolic Problems
MSC 2010: 44A35, 44A40
Exact solutions of steady plane flows using -coordinates.
Exact solutions of steady plane MHD aligned flows using - or -coordinates.