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Department of Mathematical Sciences

# Research Seminar Series

## Applied Mathematics Seminars: Homogenisation and continuous dependence of solutions of pdes on the coefficients

Presented by Marcus Waurick, University of Strathclyde

13 October 2017 14:00 in CM219

In the setting of so-called evolutionary equations invented by Rainer Picard in 2009 we identify homogenisation problems as being equivalent to a certain type of a continuity property of solution operators. Indeed, it can be shown that \$G\$-convergence of matrix-coefficients is equivalent to convergence of certain inverses in the weak operator topology. With this, one can show various homogenisation results for a wide class of standard linear equations in mathematical physics. Furthermore, the genericity of memory effects to arise due to the homogenisation process in the context Maxwell's equations can be explained by operator-theoretic means.

## Applied Mathematics Seminars: Homogenisation and continuous dependence of solutions of pdes on the coefficients

Presented by Marcus Waurick, University of Strathclyde

13 October 2017 14:00 in CM219

In the setting of so-called evolutionary equations invented by Rainer Picard in 2009 we identify homogenisation problems as being equivalent to a certain type of a continuity property of solution operators. Indeed, it can be shown that \$G\$-convergence of matrix-coefficients is equivalent to convergence of certain inverses in the weak operator topology. With this, one can show various homogenisation results for a wide class of standard linear equations in mathematical physics. Furthermore, the genericity of memory effects to arise due to the homogenisation process in the context Maxwell's equations can be explained by operator-theoretic means.

## Applied Mathematics Seminars: Homogenisation and continuous dependence of solutions of pdes on the coefficients

Presented by Marcus Waurick, University of Strathclyde

13 October 2017 14:00 in CM219

In the setting of so-called evolutionary equations invented by Rainer Picard in 2009 we identify homogenisation problems as being equivalent to a certain type of a continuity property of solution operators. Indeed, it can be shown that \$G\$-convergence of matrix-coefficients is equivalent to convergence of certain inverses in the weak operator topology. With this, one can show various homogenisation results for a wide class of standard linear equations in mathematical physics. Furthermore, the genericity of memory effects to arise due to the homogenisation process in the context Maxwell's equations can be explained by operator-theoretic means.

## Applied Mathematics Seminars: Homogenisation and continuous dependence of solutions of pdes on the coefficients

Presented by Marcus Waurick, University of Strathclyde

13 October 2017 14:00 in CM219

In the setting of so-called evolutionary equations invented by Rainer Picard in 2009 we identify homogenisation problems as being equivalent to a certain type of a continuity property of solution operators. Indeed, it can be shown that \$G\$-convergence of matrix-coefficients is equivalent to convergence of certain inverses in the weak operator topology. With this, one can show various homogenisation results for a wide class of standard linear equations in mathematical physics. Furthermore, the genericity of memory effects to arise due to the homogenisation process in the context Maxwell's equations can be explained by operator-theoretic means.

## Applied Mathematics Seminars: Homogenisation and continuous dependence of solutions of pdes on the coefficients

Presented by Marcus Waurick, University of Strathclyde

13 October 2017 14:00 in CM219

In the setting of so-called evolutionary equations invented by Rainer Picard in 2009 we identify homogenisation problems as being equivalent to a certain type of a continuity property of solution operators. Indeed, it can be shown that \$G\$-convergence of matrix-coefficients is equivalent to convergence of certain inverses in the weak operator topology. With this, one can show various homogenisation results for a wide class of standard linear equations in mathematical physics. Furthermore, the genericity of memory effects to arise due to the homogenisation process in the context Maxwell's equations can be explained by operator-theoretic means.

## Applied Mathematics Seminars: Homogenisation and continuous dependence of solutions of pdes on the coefficients

Presented by Marcus Waurick, University of Strathclyde

13 October 2017 14:00 in CM219

In the setting of so-called evolutionary equations invented by Rainer Picard in 2009 we identify homogenisation problems as being equivalent to a certain type of a continuity property of solution operators. Indeed, it can be shown that \$G\$-convergence of matrix-coefficients is equivalent to convergence of certain inverses in the weak operator topology. With this, one can show various homogenisation results for a wide class of standard linear equations in mathematical physics. Furthermore, the genericity of memory effects to arise due to the homogenisation process in the context Maxwell's equations can be explained by operator-theoretic means.

## Applied Mathematics Seminars: Homogenisation and continuous dependence of solutions of pdes on the coefficients

Presented by Marcus Waurick, University of Strathclyde

13 October 2017 14:00 in CM219

In the setting of so-called evolutionary equations invented by Rainer Picard in 2009 we identify homogenisation problems as being equivalent to a certain type of a continuity property of solution operators. Indeed, it can be shown that \$G\$-convergence of matrix-coefficients is equivalent to convergence of certain inverses in the weak operator topology. With this, one can show various homogenisation results for a wide class of standard linear equations in mathematical physics. Furthermore, the genericity of memory effects to arise due to the homogenisation process in the context Maxwell's equations can be explained by operator-theoretic means.

## Applied Mathematics Seminars: Homogenisation and continuous dependence of solutions of pdes on the coefficients

Presented by Marcus Waurick, University of Strathclyde

13 October 2017 14:00 in CM219

In the setting of so-called evolutionary equations invented by Rainer Picard in 2009 we identify homogenisation problems as being equivalent to a certain type of a continuity property of solution operators. Indeed, it can be shown that \$G\$-convergence of matrix-coefficients is equivalent to convergence of certain inverses in the weak operator topology. With this, one can show various homogenisation results for a wide class of standard linear equations in mathematical physics. Furthermore, the genericity of memory effects to arise due to the homogenisation process in the context Maxwell's equations can be explained by operator-theoretic means.

## Applied Mathematics Seminars: Homogenisation and continuous dependence of solutions of pdes on the coefficients

Presented by Marcus Waurick, University of Strathclyde

13 October 2017 14:00 in CM219

In the setting of so-called evolutionary equations invented by Rainer Picard in 2009 we identify homogenisation problems as being equivalent to a certain type of a continuity property of solution operators. Indeed, it can be shown that \$G\$-convergence of matrix-coefficients is equivalent to convergence of certain inverses in the weak operator topology. With this, one can show various homogenisation results for a wide class of standard linear equations in mathematical physics. Furthermore, the genericity of memory effects to arise due to the homogenisation process in the context Maxwell's equations can be explained by operator-theoretic means.

## Applied Mathematics Seminars: Homogenisation and continuous dependence of solutions of pdes on the coefficients

Presented by Marcus Waurick, University of Strathclyde

13 October 2017 14:00 in CM219

In the setting of so-called evolutionary equations invented by Rainer Picard in 2009 we identify homogenisation problems as being equivalent to a certain type of a continuity property of solution operators. Indeed, it can be shown that \$G\$-convergence of matrix-coefficients is equivalent to convergence of certain inverses in the weak operator topology. With this, one can show various homogenisation results for a wide class of standard linear equations in mathematical physics. Furthermore, the genericity of memory effects to arise due to the homogenisation process in the context Maxwell's equations can be explained by operator-theoretic means.

## Applied Mathematics Seminars: Homogenisation and continuous dependence of solutions of pdes on the coefficients

Presented by Marcus Waurick, University of Strathclyde

13 October 2017 14:00 in CM219

In the setting of so-called evolutionary equations invented by Rainer Picard in 2009 we identify homogenisation problems as being equivalent to a certain type of a continuity property of solution operators. Indeed, it can be shown that \$G\$-convergence of matrix-coefficients is equivalent to convergence of certain inverses in the weak operator topology. With this, one can show various homogenisation results for a wide class of standard linear equations in mathematical physics. Furthermore, the genericity of memory effects to arise due to the homogenisation process in the context Maxwell's equations can be explained by operator-theoretic means.

## Applied Mathematics Seminars: Homogenisation and continuous dependence of solutions of pdes on the coefficients

Presented by Marcus Waurick, University of Strathclyde

13 October 2017 14:00 in CM219

In the setting of so-called evolutionary equations invented by Rainer Picard in 2009 we identify homogenisation problems as being equivalent to a certain type of a continuity property of solution operators. Indeed, it can be shown that \$G\$-convergence of matrix-coefficients is equivalent to convergence of certain inverses in the weak operator topology. With this, one can show various homogenisation results for a wide class of standard linear equations in mathematical physics. Furthermore, the genericity of memory effects to arise due to the homogenisation process in the context Maxwell's equations can be explained by operator-theoretic means.