General boundary value problems are considered for general parabolic (in the Douglas–Nirenberg–Solonnikov sense) systems. The dependence of solution uniqueness classes of these problems on the geometry of a nonbounded domain is established. The dependence of solution uniqueness classes of the first boundary value problem for a second-order parabolic equation in an unbounded domain on the domain...

We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficients may depend on space and time. Pointwise convergence of the global analytic expansion is proved. This leads to analytic representations of solutions of initial-boundary problems of first and second type in terms of convol...

CONTENTS Introduction 151 § 1. Maximal attractors of semigroups generated by evolution equations 156 § 2. Examples of parabolic equations and systems having a maximal attractor 158 § 3. The Hausdorff dimension of invariant sets 164 § 4. Estimate of the change in volume under the action of shift operators generated by linear evolution equations 167 § 5. An upper bound for the Hausdorff dimension...