Gheorghe Moroșanu
Abstract. Let H be a real Hilbert space, and let A : D(A) ⸦ H → H be a (possibly multivalued) subdifferential operator. In this article we remind the most important results regarding the existence and asymptotic behavior for t → ∞ of solutions to the evolution equation (inclusion) u′(t) + Au(t) ∋ f(t), t > 0, including contributions of J.-B. Baillon, H. Brezis, R.E. Bruck, Y. K¯omura, H. Okochi, and of the au- thor. On this occasion, we show that a stability theorem of V. Barbu is in fact a particular case of a previous result of H. Brezis. Also, we extend that Brezis’ result establishing the weak convergence as t → ∞ of every (weak) solution to the above evolution inclusion.
Keywords: evolution equation, monotone operator, subdifferential op- erator, existence and asymptotic behavior of solutions as t →∞.
MSC: 34G25, 47H05, 47J35.
DOI 10.56082/annalsarscimath.2025.1.37
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics on Its Application, Volume 17 no 1, 2025
