?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4988%2F&rft.title=On+a+Problem+of+Source+Reconstruction+for+Parabolic+Equation&rft.creator=Samarskaya%2C+E.A.&rft.creator=Tishkin%2C+V.&rft.description=In+the+present+paper+the+problem+of+reconstruction+of+the+right-hand+side+of+an+advection-diffusion+equation+is+considered.+This+type+of+equation+is+used+in+many+models+of+contamination+transport+in+domains+such+as+air%2C+groundwater+and+surface+water.+Using+the+method+of+conjugate+equations%2C+one+can+reduce+the+problem+to+an+integral+equation+of+the+first+kind.+In+the+paper+a+discrete+analog+of+this+integral+equation+is+constructed+on+the+basis+of+discretization+of+the+initial+advection-diffusion+equation+and+the+usage+of+the+conjugate+equation+technique.+For+solving+the+obtained+discrete+analog+of+the+integral+equation+Tikhonov's+method+of+regularization+is+applied.+The+parameter+of+regularization+is+chosen+in+accordance+with+the+residual+principle.+Series+of+numerical+calculations+show+efficiency+of+the+method.&rft.publisher=WP-96-038&rft.date=1996-04&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4988%2F1%2FWP-96-038.pdf&rft.identifier=++Samarskaya%2C+E.A.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F2619.html%3E+%26+Tishkin%2C+V.++(1996).++On+a+Problem+of+Source+Reconstruction+for+Parabolic+Equation.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-96-038+++++