5 papers
On Riemann wave superpositions obtained from the Euler system
Łukasz Chomienia, Alfred Michel Grundland
The paper contains an analysis of the conditions for the existence of elastic versus non-elastic wave superpositions governed by the Euler system in (1+1)-dimensions. A review of r…
Nonlinear wave superpositions and quasi-rectifiable Lie modules
Łukasz Chomienia, Alfred Michel Grundland
This paper presents a study of nonlinear superpositions of Riemann wave solutions admitted by quasilinear hyperbolic first-order systems of partial differential equations. In parti…
Partial Differential Equations on Low-Dimensional Structures
Łukasz Chomienia
This thesis pertains to the study of elliptic and parabolic partial differential equations on "thin" structures. The first main objective is to establish the strong and weak low-di…
Higher regularity of solutions to elliptic equations on low-dimensional structures
Łukasz Chomienia, Michał Fabisiak
This paper aims to establish counterparts of fundamental regularity statements for solutions to elliptic equations in the setting of low-dimensional structures such as, for instanc…
Parabolic PDEs on low-dimensional structures
Łukasz Chomienia
The paper concerns the theory of parabolic equations on a broad class of closed subsets of Euclidean space possessing a kind of tangent structure. A necessary framework for conside…