Nonlocal solutions of parabolic equations with strongly elliptic differential operators
| Autor: | Luisa Malaguti, Irene Benedetti, Valentina Taddei |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
35K20 (Primary)
34B10 47H11 93D30 (Secondary) Parabolic equations Boundary (topology) Lyapunov-like functions Fixed point 01 natural sciences symbols.namesake Mathematics - Analysis of PDEs FOS: Mathematics Boundary value problem 0101 mathematics Mathematics Degree theory Dirichlet conditions Applied Mathematics 010102 general mathematics Mathematical analysis Multipoint and mean value conditions Analysis Function (mathematics) Differential operator Parabolic partial differential equation 010101 applied mathematics Bounded function symbols Analysis of PDEs (math.AP) |
| Zdroj: | Journal of Mathematical Analysis and Applications. 473:421-443 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2018.12.059 |
| Popis: | The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction–diffusion processes in several frameworks. A linear diffusion term in divergence form is included which generates a strongly elliptic differential operator. A further linear part, of integral type, is present which accounts of nonlocal diffusion behaviours. The main result provides a unifying method for studying the existence and localization of solutions satisfying nonlocal associated boundary conditions. The Cauchy multipoint and the mean value conditions are included in this investigation. The problem is transformed into its abstract setting and the proofs are based on the homotopic invariance of the Leray–Schauder topological degree. A bounding function (i.e. Lyapunov-like function) theory is developed, which is new in this infinite dimensional context. It allows that the associated vector fields have no fixed points on the boundary of their domains and then it makes possible the use of a degree argument. |
| Databáze: | OpenAIRE |
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