Higher-order parabolic equations without conditions at infinity

Admissible Conditions for Parabolic Equations Degenerating at Infinity

Well-posedness in L∞(Rn) (n ≥ 3) of the Cauchy problem is studied for a class of linear parabolic equations with variable density. In view of degeneracy at infinity, some conditions at infinity are possibly needed to make the problem well-posed. Existence and uniqueness results are proved for bounded solutions that satisfy either Dirichlet or Neumann conditions at infinity. §

Higher-order operator splitting methods for deterministic parabolic equations

Self-Similar Blow-Up in Higher-Order Semilinear Parabolic Equations

We study the Cauchy problem in R × R+ for one-dimensional 2mth-order, m > 1, semilinear parabolic PDEs of the form (Dx = ∂/∂x) ut = (−1) D x u + |u| u, where p > 1, and ut = (−1) D x u + e u with bounded initial data u0(x). Specifically, we are interested in those solutions that blow up at the origin in a finite time T . We show that, in contrast to the solutions of the classical secondorder pa...

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...