{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T10:34:07Z","timestamp":1787654047277,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>In this paper we are concerned with the global \"nonnegative\" approximate controllability property of a rather general semilinear heat equation with superlinear term, governed in a bounded domain $\\Omega \\subset R^n$ by a multiplicative (bilinear) control in the reaction term like vu (x,t), where v is the control. We show that any nonnegative target state in $L^2 (\\Omega)$ can approximately be reached from any nonnegative, nonzero initial state by applying at most three static bilinear $L^\\infty (\\Omega)$-controls subsequently in time. This result is further applied to discuss the controllability properties of the nonhomogeneous version of this problem with bilinear term like $v (u (x,t)-\\theta (x))$, where $\\theta$ is given. Ourapproach is based on an asymptotic technique allowing us to distinguish and make use of the pure diffusion and\/or pure reaction parts of the dynamics of the system at hand, while suppressing the effect of a (general) nonlinear term.<\/jats:p>","DOI":"10.1137\/s0363012901394607","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1886-1900","source":"Crossref","is-referenced-by-count":49,"title":["Controllability of the Semilinear Parabolic Equation Governed by a Multiplicative Control in the Reaction Term: A Qualitative Approach"],"prefix":"10.1137","volume":"41","author":[{"given":"A. Y.","family":"Khapalov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","volume-title":"Local stabilizability of nonlinear control systems","author":"Bacciotti Andrea","year":"1992"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01442552"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160320405"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0320042"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1999.6524"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500030742"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.57262\/ade\/1356651338"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/s0294-1449(00)00117-7"},{"key":"R9","unstructured":"L. A. 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