Evolution operators for higher order abstract parabolic equations

Nonlocal higher order evolution equations

In this paper we study the asymptotic behavior of solutions to the nonlocal operator ut(x, t) = (−1) n−1 (J ∗ Id − 1)n (u(x, t)), x ∈ R which is the nonlocal analogous to the higher order local evolution equation vt = (−1)(∆)v. We prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. Moreover, we prove that the solutions of the nonlocal problem conver...

Higher-order operator splitting methods for deterministic parabolic equations

Blow-up Estimates for Higher-order Semilinear Parabolic Equations

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...

Reduction Operators of Linear Second-Order Parabolic Equations

The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1 + 1)dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary differential ones are exhaustively described. This problem proves to be equivalent, in some sense, to solving the initial equations. The “no-go” result is extended to...