PHASE SPACE ANALYSIS OF PARTIAL DIFFERENTIAL EQUATIONS

By LINDA BROWN

STRONG UNIQUE CONTINUATION AND FINITE JET DETERMINATION FOR CAUCHY RIEMANN MAPPINGS ON THE CAUCHY PROBLEM FOR SOME HYPERBOLIC OPERATOR WITH DOUBLE CHARACTERISTICS ON THE DIFFERENTIABILITY CLASS THE ADMISSIBLE SQUARE ROOTS REGULAR NONNEGATIVE FUNCTIONS THE BENJAMIN ONO EQUATION ENERGY SPACE INSTABILITIES ZAKHAROV EQUATIONS FOR LASER PROPAGATION PLASMA SYMPLECTIC STRATA AND ANALYTIC HYPOELLIPTICITY ON THE BACKWARD UNIQUENESS PROPERTY FOR CLASS PARABOLIC OPERATORS INVERSE PROBLEMS FOR HYPERBOLIC EQUATIONS ON THE OPTIMALITY SOME OBSERVABILITY INEQUALITIES FOR PLATE SYSTEMS WITH POTENTIALS SOME GEOMETRIC EVOLUTION EQUATIONS ARISING GEODESIC EQUATIONS GROUPS DIFFEOMORPHISMS INCLUDING THE HAMILTONIAN APPROACH NON-EFFECTIVELY HYPERBOLIC OPERATORS AND BICHARACTERISTICS ON THE FEFFERMAN PHONG INEQUALITY FOR SYSTEMS PDES LOCAL ENERGY DECAY AND STRICHARTZ ESTIMATES FOR THE WAVE EQUATION WITH TIME-PERIODIC PERTURBATIONS ELEMENTARY PROOF FEDI S THEOREM AND EXTENSIONS OUTGOING PARAMETRICES AND GLOBAL STRICHARTZ ESTIMATES FOR SCHR¨ODINGER EQUATIONS WITH VARIABLE COEFFICIENTS ON THE ANALYTICITY SOLUTIONS SUMS SQUARES VECTOR FIELDS