Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 (2016), 1902–1910 Research Article Finite time blow up of solutions to an inverse problem for a quasilinear parabolic equation with power nonlinearity S ¸evket G¨ ur, Metin Yaman ∗ , Yal¸ cın Yılmaz Department of mathematics, Sakarya University, Sakarya, Turkey. Communicated by E. Savas Abstract We consider an inverse problem for quasilinear parabolic equations with type power nonlinearity. Sufficient conditions on initial data for blow up result are obtained with positive initial energy. Over- determination condition is given as an integral form. To get the blow up result for considered nonlinear inverse parabolic equation, we use the concavity of a special positive function. The life span of the solution is also computed. c 2016 All rights reserved. Keywords: Blow-up, inverse problem, quasilinear parabolic equation. 2010 MSC: 35K59, 35R30. 1. Introduction Inverse problems are the problems that consist of finding an unknown property of an object, or a medium, from the observation of a response of this object, or medium, to a probing signal. Thus, the theory of inverse problems yields a theoretical basis for remote sensing and nondestructive evaluation. For example, if an acoustic plane wave is scattered by an obstacle, and one observes the scattered field far from the obstacle, or in some exterior region, then the inverse problem is to find the shape and material properties of the obstacle. Such problems are important in identification of flying objects (airplanes, missiles, etc.), objects immersed in water (submarines, paces of fish, etc.), and in many other situations. ∗ Corresponding author Email addresses: sgur@sakarya.edu.tr (S ¸evket G¨ ur), myaman@sakarya.edu.tr (Metin Yaman), yalciny@sakarya.edu.tr (Yal¸ cın Yılmaz) Received 2015-10-09